Transactions of the AMS. Year 1955. Volume 078. Number 02.


Abelian varieties over function fields
Wei-Liang Chow
253-275


Meromorphic functions with three radially distributed values
Albert Edrei
276-293


On asymptotic values of functions analytic in a circle
Makoto Ohtsuka
294-304


Asymptotic expansions for the Whittaker functions of large complex order $m$
Nicholas D. Kazarinoff
305-328


On Burnside's problem. II
R. C. Lyndon
329-332


Some theorems on bounded analytic functions
Walter Rudin
333-342


A theory of analytic functions in Banach algebras
E. K. Blum
343-370


Note on the Fourier inversion formula on groups
F. I. Mautner
371-384


Causality and analyticity
Y. Fourès; I. E. Segal
385-405


Eigenfunction expansions associated with singular differential operators
Joanne Elliott
406-425


Hilbert space methods in the theory of harmonic integrals
Matthew P. Gaffney
426-444


The number of linear, directed, rooted, and connected graphs
Frank Harary
445-463


Difference sets in a finite group
R. H. Bruck
464-481


On the application of the individual ergodic theorem to discrete stochastic processes
H. D. Brunk
482-491


On linear, second order differential equations in the unit circle
Philip Hartman; Aurel Wintner
492-500


Summation of bounded divergent sequences, topological methods
Albert Wilansky; Karl Zeller
501-509


On Bieberbach-Eilenberg functions. II
James A. Jenkins
510-515


Strict convexity and smoothness of normed spaces
Mahlon M. Day
516-528


Some analytical properties of continuous stationary Markov transition functions
David G. Kendall
529-540

Abstract: A systematic treatment of Markov processes with Euclidean state-spaces has recently been presented by Doob [1], the restriction on the nature of the state-space being associated with the very illuminating probabilistic method which he uses throughout. At about the same time a new step was taken by Kolmogorov [4] who established for countable state-spaces the existence and finiteness of the derivative of the transition-function $ {p_{ij}}(t)$ at $t = 0 +$ when $i \ne j$. In this paper some of Doob's and Kolmogorov's results are combined and shown to be valid (when suitably formulated) for an arbitrary state-space. For the sake of a generality which proves useful in the discussion of existence theorems the transition-function $ {P_t}(x,\;A)$ is not assumed to be ``honest"; i.e., if $X$ is the state-space then it is supposed that $ {P_t}(x,\;X) \leqq 1$.


The Poisson transform
Harry Pollard
541-550