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 14, Number 2

#### Publication Date: June 1947

Inversion formulas for convolution transforms

D. V. Widder; 217-249

Sums of an even number of squares in $GF[p^n,x]$

Eckford Cohen; 251-267

Representation of $\ast$-algebras

Richard Arens; 269-282

Smallest fields over which every polynomial is solvable by radicals

B. W. Brewer; 283-287

A problem in connected finite closure algebras

William T. Puckett; 289-296

The Riemann function for $\partial^2u/\partial x\partial y+H(x+y)u=0$

Harvey Cohn; 297-304

A problem of arrangements

A. Dvoretzky and Th. Motzkin; 305-313

The asymptotic density of certain sets of real numbers

A. Dvoretzky and Th. Motzkin; 315-321

The $L^2$-solutions of linear differential equations of second order

Philip Hartman; 323-326

Groups of harmonic transformations

Edward Kasner and John De Cicco; 327-338

Partial differential equations related to rational functions of a complex variable

Edward Kasner and John De Cicco; 339-348

Functions satisfying certain partial differential equations of elliptic type and their representation

Stefan Bergman; 349-366

Hlawka’s theorem in the geometry of numbers

H. Davenport and C. A. Rogers; 367-375

La puissance de certaines classes de fonctions

F. Obreanu; 377-380

Tensor theory of invariants for the projective differential geometry of a ruled surface

Thomas C. Doyle; 381-399

Cesàro summability of orthogonal series

Min-Teh Cheng; 401-404

Summability factors of Fourier series at a given point

Min-Teh Cheng; 405-410

The Dirichlet divisor problem

Richard Bellman; 411-417

Certain generalizations of the Weierstrass approximation theorem

Edwin Hewitt; 419-427

The vanishing of Ramanujan’s function $\tau(n)$

D. H. Lehmer; 429-433

Algebraic cohomology groups and loops

Samuel Eilenberg and Saunders Mac Lane; 435-463

Abstract theory of inversion of iterated summations

L. C. Hsu; 465-473

Weak definitions of field

B. A. Bernstein; 475-482

Abstract Tauberian theorems with applications to power series and Hilbert series

D. G. Northcott; 483-502

The orthogonality of some systems of polynomials

J. Geronimus; 503-510