Infinite products which are Hilbert cubes
James E.
West
1-25
Abstract: Let $Q$ denote the Hilbert cube. It is shown that if $P$ and $P'$ are compact polyhedra of the same simple homotopy type then $P \times Q$ and
On the shrinkability of decompositions of $3$-manifolds
William L.
Voxman
27-39
Abstract: An upper semicontinuous decomposition $G$ of a metric space $M$ is said to be shrinkable in case for each covering $ \mathcal{U}$ of the union of the nondegenerate elements, for each $\varepsilon > 0$, and for an arbitrary homeomorphism $h$ from $M$ onto $M$, there exists a homeomorphism $f$ from $M$ onto itself such that (1) if $ x \in M - ( \cup \{ U:U \in \mathcal{U}\} )$, then $ f(x) = h(x)$, (2) for each $g \in G$, (a) $\operatorname{diam} f[g] < \varepsilon$ and (b) there exists $ D \in \mathcal{U}$ such that $ h[D] \supset h[g] \cup f[g]$. Our main result is that if $G$ is a cellular decomposition of a $ 3$-manifold $M$, then $M/G = M$ if and only if $G$ is shrinkable. We also define concepts of local and weak shrinkability, and we show the equivalence of the various types of shrinkability for certain cellular decompositions. Some applications of these notions are given, and extensions of theorems of Bing and Price are proved.
Polynomial approximation on compact manifolds and homogeneous spaces
David L.
Ragozin
41-53
Abstract: We prove several theorems which relate the smoothness of a function, $ f$, defined on a compact ${C^\infty }$-submanifold of a Euclidean space to the rate at which the error in the best uniform approximation to $f$ by polynomials of degree at most $ n$ tends to zero.
Commutators modulo the center in a properly infinite von Neumann algebra
Herbert
Halpern
55-68
Coefficient estimates for Dirichlet series
W. T.
Sledd
69-76
An abstract nonlinear Cauchy-Kovalevska theorem
François
Trèves
77-92
Abstract: A nonlinear version of Ovcyannikov's theorem is proved. If $F(u,t)$ is an analytic function of $ t$ real or complex and of $ u$ varying in a scale of Banach spaces, valued in a scale of Banach spaces, the Cauchy problem ${u_t} = F(u,t),u(0) = {u_0}$, has a unique analytic solution. This is an abstract version of the Cauchy-Kovalevska theorem which can be applied to equations other than partial-differential, e.g. to certain differential-convolution or, more generally, differential-pseudodifferential equations.
Twin-convergence regions for continued fractions $K(a\sb{n}/1)$
William B.
Jones;
W. J.
Thron
93-119
Subgroups and automorphisms of extended Schottky type groups
Vicki
Chuckrow
121-129
On expansive transformation groups
Ping-fun
Lam
131-138
Rings for which certain flat modules are projective
S. H.
Cox;
R. L.
Pendleton
139-156
On successive approximations in homological algebra
V. K. A. M.
Gugenheim;
R. J.
Milgram
157-182
Theorems of Krein-Milman type for certain convex sets of operators.
P. D.
Morris;
R. R.
Phelps
183-200
Abstract: Let $M$ be a real (or complex) Banach space and $C(Y)$ the space of continuous real (or complex) functions on the compact Hausdorff space $ Y$. The unit ball of the space of bounded operators from $M$ into $C(Y)$ is shown to be the weak operator (or equivalently, strong operator) closed convex hull of its extreme points, provided $Y$ is totally disconnected, or provided ${M^ \ast }$ is strictly convex. These assertions are corollaries to more general theorems, most of which have valid converses. In the case $M = C(X)$, similar results are obtained for the positive normalized operators. Analogous results are obtained for the unit ball of the space of compact operators (this time in the operator norm topology) from $ M$ into $C(Y)$.
Elements with trivial centralizer in wreath products
Wolfgang P.
Kappe;
Donald B.
Parker
201-212
Abstract: Groups with self-centralizing elements have been investigated in recent papers by Kappe, Konvisser and Seksenbaev. In particular, if $G = A$wr$B$ is a wreath product some necessary and some sufficient conditions have been given for the existence of self-centralizing elements and for $G = \left\langle {{S_G}} \right\rangle$, where ${S_G}$ is the set of self-centralizing elements. In this paper ${S_G}$ and the set ${R_G}$ of elements with trivial centralizer are determined both for restricted and unrestricted wreath products. Based on this the size of $\left\langle {{S_G}} \right\rangle$ and $ \left\langle {{R_G}} \right\rangle$ is found in some cases, in particular if $ A$ and $B$ are $p$-groups or if $B$ is not periodic.
Finitely generated ideals of differentiable functions
B.
Roth
213-225
Abstract: In some spaces of differentiable functions, the finitely generated ideals which are closed are characterized in terms of the zeros of the generators. Applications are made to problems of division for distributions.
The subgroups of a free product of two groups with an amalgamated subgroup
A.
Karrass;
D.
Solitar
227-255
Abstract: We prove that all subgroups $H$ of a free product $G$ of two groups $A,B$ with an amalgamated subgroup $U$ are obtained by two constructions from the intersection of $H$ and certain conjugates of $A,B$, and $U$. The constructions are those of a tree product, a special kind of generalized free product, and of a Higman-Neumann-Neumann group. The particular conjugates of $ A,B$, and $U$ involved are given by double coset representatives in a compatible regular extended Schreier system for $G$ modulo $H$. The structure of subgroups indecomposable with respect to amalgamated product, and of subgroups satisfying a nontrivial law is specified. Let $ A$ and $B$ have the property $P$ and $U$ have the property $Q$. Then it is proved that $G$ has the property $P$ in the following cases: $ P$ means every f.g. (finitely generated) subgroup is finitely presented, and $ Q$ means every subgroup is f.g.; $P$ means the intersection of two f.g. subgroups is f.g., and $Q$ means finite; $P$ means locally indicable, and $ Q$ means cyclic. It is also proved that if $N$ is a f.g. normal subgroup of $G$ not contained in $U$, then $NU$ has finite index in $G$.
A fundamental solution of the parabolic equation on Hilbert space. II. The semigroup property
M. Ann
Piech
257-286
Abstract: The existence of a family of solution operators $\{ {q_t}:t > 0\}$ corresponding to a fundamental solution of a second order infinite-dimensional differential equation of the form $\partial u/\partial t = Lu$ was previously established by the author. In the present paper, it is established that these operators are nonnegative, and satisfy the condition ${q_s}{q_t} = {q_{s + t}}$.
Embeddings in division rings
John
Dauns
287-299
Abstract: A method for embedding a certain class of integral domains in division rings is devised. Integral domains $A$ are constructed with a generalized valuation into a (noncommutative) totally ordered semigroup that need not be discrete. Then the multiplicative semigroup $ A\backslash \{ 0\}$ is expressed as an inverse limit of semigroups each of which is embeddable in a group. Thus $A\backslash \{ 0\}$ can be embedded in a group $ G$. The main problem is to introduce addition on $G$ in order that $G$ becomes a division ring by the use of eventually commuting maps of inverse limits.
A characterization of integral currents
John E.
Brothers
301-325
Two methods of integrating Monge-Amp\`ere's equations
Michihiko
Matsuda
327-343
Abstract: Modifying Monge's method and Laplace's one respectively, we shall give two methods of integration of Monge-Ampère's equations. Although they seem quite different, the equivalence of our two methods will be shown. The first method will be from a point of view different from that of Lewy. The second will present a solution to a problem of Goursat.