Class groups of integral group rings
I.
Reiner;
S.
Ullom
1-30
Abstract: Let $\Lambda$ be an $R$-order in a semisimple finite dimensional $ K$-algebra, where $ K$ is an algebraic number field, and $R$ is the ring of algebraic integers of $ K$. Denote by $C(\Lambda )$ the reduced class group of the category of locally free left $\Lambda$-lattices. Choose $\Lambda = ZG$, the integral group ring of a finite group $G$, and let $\Lambda '$ be a maximal $Z$-order in $QG$ containing $\Lambda$. There is an epimorphism $ D(\Lambda )$ be the kernel of this epimorphism; the groups $D(\Lambda ),C(\Lambda )$ and
Second-order time degenerate parabolic equations
Margaret C.
Waid
31-55
Abstract: We study the degenerate parabolic operator $Lu = \sum\nolimits_{i,j = 1}^n {{a^{ij}}{u_{{x_j}{x_j}}}} + \sum\nolimits_{i = 1}^n {{b^i}{u_{{x_i}}}} - c{u_t} + du$ where the coefficients of $ L$ are bounded, real-valued functions defined on a domain $D = \Omega \times (0,T] \subset {R^{n + 1}}$. Classically, $ c(x,t) \equiv 1$ or, equivalently, $ c(x,t) \geq \eta > 0$ for all $(x,t) \in \bar D$. We assume only that $ c$ is non-negative. We prove weak maximum principles and Harnack inequalities. Assume that ${a^{ij}}$ is constant, the coefficients of $ L$ and $f$ and their derivatives with respect to time are uniformly Hölder continuous (exponent $\alpha$) in $ \bar D,\bar D$ has sufficiently nice boundary, $c > 0$ on the normal boundary of $D$, $\psi \in {\bar C_{z + \alpha}}$, and $ L\psi = f$ on $ \partial B = \partial (\bar D \cap \{ t = 0\} )$. Then there exists a unique solution $u$ of the first initial-boundary value problem $Lu = f,u = \psi $ on $\bar B + (\partial B \times [0,T])$; and, furthermore, $u \in {\bar C_{2 + \alpha}}$. All results require proofs that differ substantially from the classical ones.
Stone's topology for pseudocomplemented and bicomplemented lattices
P. V.
Venkatanarasimhan
57-70
Abstract: In an earlier paper the author has proved the existence of prime ideals and prime dual ideals in a pseudocomplemented lattice (not necessarily distributive). The present paper is devoted to a study of Stone's topology on the set of prime dual ideals of a pseudocomplemented and a bicomplemented lattice. If $\hat L$ is the quotient lattice arising out of the congruence relation defined by $a \equiv b \Leftrightarrow {a^ \ast } = {b^ \ast }$ in a pseudocomplemented lattice $ L$, it is proved that Stone's space of prime dual ideals of $\hat L$ is homeomorphic to the subspace of maximal dual ideals of $L$.
Approximation in operator algebras on bounded analytic functions
M. W.
Bartelt
71-83
Abstract: Let $B$ denote the algebra of bounded analytic functions on the open unit disc in the complex plane. Let $(B,\beta )$ denote $B$ endowed with the strict topology $ \beta$. In 1956, R. C. Buck introduced $ [\beta :\beta ]$, the algebra of all continuous linear operators from $(B,\beta )$ into $ (B,\beta )$. This paper studies the algebra $ [\beta :\beta ]$ and some of its subalgebras, in the norm topology and in the topology of uniform convergence on bounded subsets. We also study a special class of operators, the translation operators. For $\phi$ an analytic map of the open unit disc into itself, the translation operator ${U_\phi }$ is defined on $B$ by $ {U_\phi }f(x) = f(\phi x)$. In particular we obtain an expression for the norm of the difference of two translation operators.
Approximating embeddings of polyhedra in codimension three
J. L.
Bryant
85-95
Abstract: Let $P$ be a $p$-dimensional polyhedron and let $Q$ be a PL $q$-manifold without boundary. (Neither is necessarily compact.) The purpose of this paper is to prove that, if $q - p \geqslant 3$, then any topological embedding of $P$ into $Q$ can be pointwise approximated by PL embeddings. The proof of this theorem uses the analogous result for embeddings of one PL manifold into another obtained by Černavskiĭ and Miller.
Primitive ideals of $C\sp{\ast} $-algebras associated with transformation groups
Elliot C.
Gootman
97-108
Abstract: We extend results of E. G. Effros and F. Hahn concerning their conjecture that if $(G,Z)$ is a second countable locally compact transformation group, with $G$ amenable, then every primitive ideal of the associated ${C^ \ast }$-algebra arises as the kernel of an irreducible representation induced from an isotropy subgroup. The conjecture is verified if all isotropy subgroups lie in the center of $G$ and either (a) the restriction of each unitary representation of $G$ to some open subgroup contains a one-dimensional subrepresentation, or (b) $G$ has an open abelian subgroup and orbit closures in $Z$ are compact and minimal.
The separable closure of some commutative rings
Andy R.
Magid
109-124
Abstract: The separable closure of a commutative ring with an arbitrary number of idempotents is defined and its Galois theory studied. Projective separable algebras over the ring are shown to be determined by the 'Galois groupoid' of the closure. The existence of the closure is demonstrated for certain rings.
Projective moduli and maximal spectra of certain quotient rings
Aron
Simis
125-136
Abstract: The projective modulus of a (commutative) ring is defined and a class of quotient rings is given for which the projective moduli are arbitrarily smaller than the dimension of the maximal spectra. Families of prime ideals of Towber and maximal type are introduced herein.
An eigenfunction expansion for a nonselfadjoint, interior point boundary value problem
Allan M.
Krall
137-147
Abstract: Under discussion is the vector system $ \sum\nolimits_{j = 0}^\infty {\vert\vert A\vert\vert < \infty }$. The eigenvalues for the system are known to be countable and approach $\infty$ in the complex plane in a series of well-defined vertical steps. For each eigenvalue there exists an eigenmanifold, generated by the residue of the Green's function. Further, since the Green's function vanishes near $\infty$ in the complex plane when the path toward $ \infty$ is horizontal, the Green's function can be expressed as a series of its residues. This in turn leads to two eigenfunction expansions, one for elements in the domain of the original system, another for elements in the domain of the adjoint system.
Extreme limits of compacta valued functions
T. F.
Bridgland
149-163
Abstract: Let $X$ denote a topological space and $\Omega (X)$ the space of all nonvoid closed subsets of $X$. Recent developments in analysis, especially in control theory, have rested upon the properties of the space $\Omega (X)$ where $X$ is assumed to be metric but not necessarily compact and with $ \Omega (X)$ topologized by the Hausdorff metric. For a continuation of these developments, it is essential that definitions of extreme limits of sequences in $ \Omega (X)$ be formulated in such a way that the induced limit is topologized by the Hausdorff metric. It is the purpose of this paper to present the formulation of such a definition and to examine some of the ramifications thereof. In particular, we give several theorems which embody ``estimates of Fatou'' for integrals of set valued functions.
Norm of a derivation on a von Neumann algebra
P.
Gajendragadkar
165-170
Abstract: A derivation on an algebra $ \mathfrak{A}$ is a linear function $\mathcal{D}:\mathfrak{A} \to \mathfrak{A}$ satisfying $\mathcal{D}(ab) = \mathcal{D}(a)b + a\mathcal{D}(b)$ for all $a,b$ in $ \mathfrak{A}$. If there exists an $a$ in $ \mathfrak{A}$ such that $\mathcal{D}(b) = ab - ba$ for $ b$ in $\mathfrak{A}$, then $ \mathcal{D}$ is called the inner derivation induced by $a$. If $ \mathfrak{A}$ is a von Neumann algebra, then by a theorem of Sakai [7], every derivation on $ \mathfrak{A}$ is inner. In this paper we compute the norm of a derivation on a von Neumann algebra. Specifically we prove that if $\mathfrak{A}$ is a von Neumann algebra acting on a separable Hilbert space $\mathcal{H},T$ is in $ \mathfrak{A}$, and ${\mathcal{D}_T}$ is the derivation induced by $ T$, then $ \vert\vert{\mathcal{D}_T}\vert\mathfrak{A}\vert\vert = 2\inf \{ \vert\vert T - Z\vert\vert,Z\;{\text{in}}\;{\text{centre}}\;\mathfrak{A}\} $.
Converse theorems and extensions in Chebyshev rational approximation to certain entire functions in $[\ast \ast \ast w(\ast \ast 0,\,+\infty )\ast \ast \ast w\ast \ast $
G.
Meinardus;
A. R.
Reddy;
G. D.
Taylor;
R. S.
Varga
171-185
Abstract: Recent interest in rational approximations to $ {e^{ - x}}$ in $[0, + \infty )$, arising naturally in numerical methods for approximating solutions of heat-conduction-type parabolic differential equations, has generated results showing that the best Chebyshev rational approximations to ${e^{ - x}}$, and to reciprocals of certain entire functions, have errors for the interval $[0, + \infty )$ which converge geometrically to zero. We present here some related converse results in the spirit of the work of S. N. Bernstein.
Solid $k$-varieties and Henselian fields
Gustave
Efroymson
187-195
Abstract: Let $k$ be a field with a nontrivial absolute value. Define property $( \ast )$ for $k$: Given any polynomial $f(x)$ in $k[x]$ with a simple root $\alpha$ in $k$; then if $g(x)$ is a polynomial near enough to $ f(x),g(x)$ has a simple root $\beta$ near $\alpha$. A characterization of fields with property $( \ast )$ is given. If $Y$ is an affine $k$-variety, $ Y \subset {\bar k^{(n)}}$, define $ {Y_k} = Y \cap {k^{(n)}}$. Define $Y$ to be solid if $I(Y) = I({Y_k})$ in $k[{x_1}, \cdots ,{x_n}]$. If $\pi :Y \to {\bar k^d}$ is a projection induced by Noether normalization, and if $k$ has property $( \ast )$, then $Y$ is a solid $k$-variety if and only if $\pi ({Y_k})$ contains a sphere in ${k^d}$. Using this characterization of solid $k$-varieties and Bertini's theorem, a dimension theorem is proven.
Operators on tensor products of Banach spaces
Takashi
Ichinose
197-219
Abstract: The present paper is a study of operators on tensor products of Banach spaces with the notion of maximal extensions introduced by G. Köthe such that the closure of a closable operator is its unique maximal extension. For a class of such operators the spectral mapping theorem is established. The results apply to the operator $A \otimes I + I \otimes B$ and give a new meaning to the method of separation of variables.
Invariant polynomials on Lie algebras of inhomogeneous unitary and special orthogonal groups
S. J.
Takiff
221-230
Abstract: The ring of invariant polynomials for the adjoint action of a Lie group on its Lie algebra is described for the inhomogeneous unitary and special orthogonal groups. In particular a new proof is given for the fact that this ring for the inhomogeneous Lorentz group is generated by two algebraically independent homogeneous polynomials of degrees two and four.
Non-Hopfian groups with fully invariant kernels. I
Michael
Anshel
231-237
Abstract: Let $\mathcal{L}$ consist of the groups $G(l,m) = (a,b;{a^{ - 1}}{b^l}a = {b^m})$ where $ \vert l\vert \ne 1 \ne \vert m\vert,lm \ne 0$ and $l,m$ are coprime. We characterize the endomorphisms of these groups, compute the centralizers of special elements and show that the endomorphism $a \to a,b \to {b^l}$ is onto with a nontrivial fully invariant kernel. Hence $G(l,m)$ is non-Hopfian in the'fully invariant sense.'
Remarks on the wave front of a distribution
Akiva
Gabor
239-244
Abstract: Basic facts about composition and multiplication of distributions as given in [1] are proved using the formulas for the wave front set of the image and pullback of distributions.
Regular semigroups satisfying certain conditions on idempotents and ideals
Mario
Petrich
245-267
Abstract: The structure of regular semigroups is studied (1) whose poset of idempotents is required to be a tree or to satisfy a weaker condition concerning the behavior of idempotents in different $\mathcal{D}$-classes, or (2) all of whose ideals are categorical or satisfy a variation thereof. For this purpose the notions of $D$-majorization of idempotents, where $ D$ is a $\mathcal{D}$-class, $ \mathcal{D}$-majorization, $\mathcal{D}$-categorical ideals, and completely semisimple semigroups without contractions are introduced and several connections among them are established. Some theorems due to G. Lallement concerning subdirect products and completely regular semigroups and certain results of the author concerning completely semisimple inverse semigroups are either improved or generalized.
Maximal regular right ideal space of a primitive ring
Kwangil
Koh;
Jiang
Luh
269-277
Abstract: If $R$ is a ring, let $X(R)$ be the set of maximal regular right ideals of $R$ and $ \mathfrak{L}(R)$ be the lattice of right ideals. For each $A \in \mathfrak{L}(R)$, define $ \operatorname{supp} (A) = \{ I \in X(R)\vert A \nsubseteq I\}$. We give a topology to $X(R)$ by taking $\{ \operatorname{supp} (A)\vert A \in \mathfrak{L}(R)\}$ as a subbase. Let $R$ be a right primitive ring. Then $X(R)$ is the union of two proper closed sets if and only if $R$ is isomorphic to a dense ring with nonzero socle of linear transformations of a vector space of dimension two or more over a finite field. $X(R)$ is a Hausdorff space if and only if either $R$ is a division ring or $R$ modulo its socle is a radical ring and $ R$ is isomorphic to a dense ring of linear transformations of a vector space of dimension two or more over a finite field.
Products of weakly-$\aleph $-compact spaces
Milton
Ulmer
279-284
Abstract: A space is said to be weakly- $ {\aleph _1}$ -compact (or weakly-Lindelöf) provided each open cover admits a countable subfamily with dense union. We show this property in a product space is determined by finite subproducts, and by assuming that ${2^{{\aleph _0}}} = {2^{{\aleph _1}}}$ we show the property is not preserved by finite products. These results are generalized to higher cardinals and two research problems are stated.
Invariant means on a class of von Neumann algebras
P. F.
Renaud
285-291
Abstract: For $G$ a locally compact group with associated von Neumann algebra $VN(G)$ we prove the existence of an invariant mean on $VN(G)$. This mean is shown to be unique if and only if $G$ is discrete.
Homology in varieties of groups. IV
C. R.
Leedham-Green;
T. C.
Hurley
293-303
Abstract: The study of homology groups ${\mathfrak{B}_n}(\Pi ,A),\mathfrak{B}$ a variety, $\Pi$ a group in $ \mathfrak{B}$, and $ A$ a suitable $ \Pi$-module, is continued. A 'Tor' is constructed which gives a better (but imperfect) approximation to these groups than a Tor previously considered. ${\mathfrak{B}_2}(\Pi ,Z)$ is calculated for various varieties $ \mathfrak{B}$ and groups $ \Pi$.
Infinite dimensional Jordan operators and Sturm-Liouville conjugate point theory
J. William
Helton
305-331
Abstract: This article concerns two simple types of bounded operators with real spectrum on a Hilbert space $H$. The purpose of this note is to suggest an abstract algebraic characterization for these operators and to point out a rather unexpected connection between such algebraic considerations and the classical theory of ordinary differential equations. Now some definitions. A Jordan operator has the form $S + N$ where $S$ is selfadjoint, ${N^2} = 0$, and $S$ commutes with $N$. A sub-Jordan operator is the restriction of a Jordan operator $J$ to an invariant subspace of $J$. A coadjoint operator $ T$ satisfies ${e^{ - is{T^ \ast }}}{e^{isT}} = I + {A_1}s + {A_2}{s^2}$ for some operators ${A_1}$ and ${A_2}$ or equivalently $ {T^{ \ast 3}} - 3{T^{ \ast 2}}T + 3{T^ \ast }{T^2} - {T^3} = 0$. The main results are Theorem A. An operator $ T$ is Jordan if and only if both $T$ and ${T^ \ast }$ are coadjoint. Theorem B. If $T$ is coadjoint, if $T$ has a cyclic vector, and if $\sigma (T) = [a,b]$, then $T$ is unitarily equivalent to ' multiplication by $x$' on a weighted Sobolev space of order 1 which is supported on $[a,b]$. Theorem C. If $ T$ is coadjoint and satisfies additional technical assumptions, then $ T$ is a sub-Jordan operator. Let us discuss Theorem C. Its converse, every sub-Jordan operator is coadjoint, is easy to prove. The proof of Theorem C consists of using Theorem B to reduce Theorem C to a question about ordinary differential equations which can be solved by an exacting application of the Jacobi conjugate point theorem for Sturm-Liouville operators. The author suspects that Theorem C is itself related to the conjugate point theorem.
Deformations of integrals of exterior differential systems
Dominic S. P.
Leung
333-358
Abstract: On any general solution of an exterior differential system $ I$, a system of linear differential equations, called the equations of variation of $I$, is defined. Let $ {\text{v}}$ be a vector field defined on a general solution of $I$ such that it satisfies the equations of variation and wherever it is defined, ${\text{v}}$ is either the zero vector or it is not tangential to the general solution. By means of some associated differential systems and the fundamental theorem of Cartan-Kähler theory, it is proved that, under the assumption of real analyticity, ${\text{v}}$ is locally the deformation vector field of a one-parameter family of general solutions of $I$. As an application, it is proved that, under the assumption of real analyticity, every Jacobi field on a minimal submanifold of a Riemannian manifold is locally the deformation vector field of a one-parameter family of minimal submanifolds.
Limit behavior of solutions of stochastic differential equations
Avner
Friedman
359-384
Abstract: Consider a system of $m$ stochastic differential equations $ d\xi = a(t,\xi )dt + \sigma (t,\xi )dw$. The limit behavior of $\xi (t)$, as $t \to \infty$, is studied. Estimates of the form $ E\vert\xi (t) - \bar \sigma w(t){\vert^2} = O({t^{1 - \delta }})$ are derived, and various applications are given.
On Knaster's conjecture
R. P.
Jerrard
385-402
Abstract: Knaster's conjecture is: given a continuous $g:{S^n} \to {E^m}$ and a set $\Delta$ of $n - m + 2$ distinct points $({q_1}, \ldots ,{q_{n - m + 2}})$ in ${S^n}$ there exists a rotation $r:{S^n} \to {S^n}$ such that $\displaystyle g(r({q_1})) = g(r({q_2})) = \cdots = g(r({q_{n - m + 2}})).$ We prove a stronger statement about a smaller class of functions. If $f:{S^n} \to {E^n}$ we write $f = ({f_1},{f_2}, \ldots ,{f_n})$ where ${f_i}:{S^n} \to {E^1}$, and put $ {F_i} = ({f_1}, \ldots ,{f_i}):{S^n} \to {E^i}$ so that ${F_n} = f$. The level surface of $ {F_i}$ in ${S^n}$ containing $x$ is ${l_i}(x) = \{ y \in {S^n}\vert{F_i}(x) = {F_i}(y)\}$. Theorem. Given an $(n + 1)$-frame $\Delta \subset {S^n}$ and a real-analytic function $f:{S^n} \to {E^n}$ such that each $ {l_i}(x)$ is either a point or a topological $(n - i)$-sphere, there exist at least ${2^{n - 1}}$ distinct rotations $r:{S^n} \to {S^n}$ such that $\displaystyle {f_i}(r({q_1})) = \cdots = {f_i}(r({q_{n - i + 2}})),\quad i = 1,2, \ldots ,n,$ for each rotation. It follows that for $m = 1,2, \ldots ,n$, $\displaystyle {F_m}(r({q_1})) = {F_m}(r({q_2})) = \cdots = {F_m}(r({q_{n - m + 2}})),$ so that the functions ${F_m}:{S^n} \to {E^m}$ satisfy Knaster's conjecture simultaneously. Given ${F_i}$, the definition of $f$ can be completed in many ways by choosing ${f_{i + 1}}, \cdots ,{f_n}$, each way giving rise to different rotations satisfying the Theorem. A suitable homotopy of $f$ which changes ${f_n}$ slightly will give locally a continuum of rotations $r$ each of which satisfies Knaster's conjecture for ${F_{n - 1}}$. In general there exists an $ (n - m)$-dimensional family of rotations satisfying Knaster's conjecture for $ {F_m}$.
The completion of an abelian category
H. B.
Stauffer
403-414
Abstract: Any category $\underline{A}$ can be embedded in its right completion $ \underline{\hat{A}}$. When $\underline{A}$ is small and abelian, this completion $ \underline{\hat{A}}$ is AB5 and the embedding is exact.
Piecewise linear critical levels and collapsing
C.
Kearton;
W. B. R.
Lickorish
415-424
Abstract: In this paper the idea of collapsing, and the associated idea of handle cancellation, in a piecewise linear manifold are used to produce a version of Morse theory for piecewise linear embeddings. As an application of this it is shown that, if $n > 2$, there exist triangulations of the $ n$-ball that are not simplicially collapsible.
Exponential decay of weak solutions for hyperbolic systems of first order with discontinuous coefficients
Hang Chin
Lai
425-436
Abstract: The weak solution of the Cauchy problem for symmetric hyperbolic systems with discontinuous coefficients in several space variables satisfying the fact that the coefficients and their first derivatives are bounded in the distribution sense is identically equal to zero if it is exponential decay.
Rings with property $D$
Eben
Matlis
437-446
Abstract: An integral domain is said to have property $ {\text{D}}$ if every torsion-free module of finite rank is a direct sum of modules of rank one. In recent papers the author has given partial solutions to the problem of finding all rings with this property. In this paper the author is finally able to show that an integrally closed integral domain has property $ {\text{D}}$ if and only if it is the intersection of at most two maximal valuation rings.
$m$-symplectic matrices
Edward
Spence
447-457
Abstract: The symplectic modular group $ \mathfrak{M}$ is the set of all $2n \times 2n$ matrices $M$ with rational integral entries, which satisfy $n \times n$ matrix. Let $m$ be a positive integer. Then the $2n \times 2n$ matrix $N$ is said to be $m$-symplectic if it has rational integral entries and if it satisfies $NJN' = mJ$. In this paper we consider canonical forms for $m$-symplectic matrices under left-multiplication by symplectic modular matrices (corresponding to Hermite's normal form) and under both left- and right-multiplication by symplectic modular matrices (corresponding to Smith's normal form). The number of canonical forms in each case is determined explicitly in terms of the prime divisors of $m$. Finally, corresponding results are stated, without proof, for 0-symplectic matrices; these are $2n \times 2n$ matrices $M$ with rational integral entries and which satisfy $ MJM' = M'JM = 0$.
Strictly irreducible $\sp{\ast} $-representations of Banach $\sp{\ast} $-algebras
Bruce A.
Barnes
459-469
Abstract: In this paper strictly irreducible $\ast$-representations of Banach $\ast $-algebras and the positive functionals associated with these representations are studied.
Exterior powers and torsion free modules over discrete valuation rings
David M.
Arnold
471-481
Abstract: Pure $R$-submodules of the $p$-adic completion of a discrete valuation ring $R$ with unique prime ideal $(p)$ (called purely indecomposable $ R$-modules) have been studied in detail. This paper contains an investigation of a new class of torsion free $R$-modules of finite rank (called totally indecomposable $R$-modules) properly containing the class of purely indecomposable $R$-modules of finite rank. Exterior powers are used to construct examples of totally indecomposable modules.
Sequences of convergence regions for continued fractions $K(a\sb{n}/1)$
William B.
Jones;
R. I.
Snell
483-497
Abstract: Sufficient conditions are given for convergence of continued fractions $K({a_n}/1)$ such that ${a_n} \in {E_n},n \geqslant 1$, where $\{ {E_n}\}$ is a sequence of element regions in the complex plane. The method employed makes essential use of a nested sequence of circular disks (inclusion regions), such that the $n$th disk contains the $n$th approximant of the continued fraction. This sequence can either shrink to a point, the limit point case, or to a disk, the limit circle case. Sufficient conditions are determined for convergence of the continued fraction in the limit circle case and these conditions are incorporated in the element regions ${E_n}$. The results provide new criteria for a sequence $\{ {E_n}\}$ with unbounded regions to be an admissible sequence. They also yield generalizations of certain twin-convergence regions.
The number of roots in a simply-connected $H$-manifold
Robert F.
Brown;
Ronald J.
Stern
499-505
Abstract: An $H$-manifold is a triple $(M,m,e)$ where $M$ is a compact connected triangulable manifold without boundary, $e \in M$, and $ m:M \times M \to M$ is a map such that $ m(x,e) = m(e,x) = x$ for all $x \in M$. Define $ {m_1}:M \to M$ to be the identity map and, for $ k \geqslant 2$, define ${m_k}:M \to M$ by ${m_k}(x) = m(x,{m_{k - 1}}(x))$. It is proven that if $(M,m,e)$ is an $H$-manifold, then $M$ is simply-connected if and only if given $k \geqslant 1$ there exists a multiplication $ m'$ on $M$ homotopic to $m$ such that $j \leqslant k$.
Erratum: ``Subordination principle and distortion theorems on holomorphic mappings in the space $C\sp{n}$'' (Trans. Amer. Math. Soc. {\bf 162} (1971), 327--336)
Kyong T.
Hahn
507-508