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