Transactions of the AMS. Year 1968. Volume 130. Number 01.


On the lattice of recursively enumerable sets
A. H. Lachlan
1-37


Computable algebraic structures and nonstandard arithmetic
Eugene W. Madison
38-54


On a necessary condition for the validity of the Riemann hypothesis for functions that generalize the Riemann zeta function
Ronald Alter
55-74


Families of finite character and essential valuations
Malcolm Griffin
75-85


Absolutely closed spaces
Chen-tung Liu
86-104


The formal linearization of a semisimple Lie algebra of vector fields about a singular point
Robert Hermann
105-109

Abstract: A classical theorem by Poincaré gives conditions that a nonlinear ordinary differential equation $\displaystyle dx/dt = A(x),$ with $A(0) = 0$ in n variables $x = ({x_1}, \ldots ,{x_n})$ can be reduced to a linear form $\displaystyle \frac{{dx'}}{{dt}} = \frac{{\partial A}}{{\partial x}}(0)x'$ by a change of variables $x' = f(x)$. A generalization is given for a finite set of such differential equations, which form a semisimple Lie algebra.


Remarks on a paper of Hermann
Victor W. Guillemin; Shlomo Sternberg
110-116


Function algebras, means, and fixed points
Theodore Mitchell
117-126


Invariant means and fixed points: A sequel to Mitchell's paper
L. N. Argabright
127-130


Addition and reduction theorems for medial properties
R. L. Wilder
131-140


Infinite-product Markov processes
T. E. Harris
141-152


Irreducible Jordan algebras of self-adjoint operators
Erling Størmer
153-166


The convergence of sequences of rational functions of best approximation. III
J. L. Walsh
167-183


Correction to ``Measurable gambling houses''
Ralph E. Strauch
184