Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. Without specializing in a small number of subject areas, it emphasizes the most active and influential areas of current mathematics.

### Volume 25, Number 1

#### Publication Date: March 1958

Congruence properties of the classical orthogonal polynomials

W. A. Al-Salam and L. Carlitz; 1-9

Retracts from neighborhood retracts

W. L. Strother and L. E. Ward, Jr.; 11-14

Kernel functions and eigenfunction expansions

Edward Nelson; 15-27

Stirling numbers of the second kind

L. Moser and M. Wyman; 29-43

An extension of E. Hopf’s maximum principle with an application to Riemannian geometry

E. Calabi; 45-56

Hölder continuity and non-linear elliptic partial differential equations

Philip Hartman; 57-65

Proof of a conjecture of Grosswald

Paul T. Bateman; 67-72

A generalization of Lommel polynomials

A. M. Chak; 73-82

Some properties of compactifications

Melvin Henriksen and J. R. Isbell; 83-105

A characterization of the classical groups

Bertram Kostant; 107-123

The harmonic summation of the derived Fourier series

P. C. Rath; 125-130

Spectral invariance of convolution operators on $L^p(-\infty,\infty)$

G. L. Krabbe; 131-141

Local operators on Fourier transforms

Louis de Branges; 143-153

Congruence properties of the solutions of certain difference equations

J. Robert Johnson, Jr.; 155-170

Series of Legendre and Laguerre polynomials

V. F. Cowling; 171-176

The square root set of a simple basic set of polynomials

M. N. Mikhail; 177-180

Transforms of Tauberian series by Riesz methods of different orders

Morris Tenenbaum; 181-191