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 26, Number 4

#### Publication Date: December 1959

Functions with positive real part and Schlicht functions

S. D. Bernardi; 541-548

A theorem on the measurability of group-invariant operators

I. E. Segal; 549-552

The vanishing of the homogeneous product sum of the roots of a cubic

Morgan Ward; 553-562

Relations among the minors of a matrix with dominant principal diagonal

J. L. Brenner; 563-567

The numbers generated by ${\rm exp}({\rm arctan} x)$

Richard Kelisky; 569-581

Some arithmetic properties of a special sequence of polynomials

L. Carlitz; 583-590

Expansions in series of homogeneous polynomial solutions of the two-dimensional wave equation

D. V. Widder; 591-598

Expansions in series of homogeneous polynomial solutions of the general two-dimensional linear partial differential equation of the second order with constant coefficients

D. V. Widder; 599-603

The analogue for maximally convergent polynomials of Jentzsch’s theorem

J. L. Walsh; 605-616

Positive definite sequences and absolutely monotonic functions

Walter Rudin; 617-622

Characteristically nilpotent Lie algebras

G. Leger and S. Tôgô; 623-628

Concerning the Hausdorff inclusion problem

J. H. Wells; 629-645

A theorem on semi-continuous set-valued functions

E. Michael; 647-651

The greatest distance between two characteristic roots of a matrix

Alfred Brauer and A. C. Mewborn; 653-661

Investigation concerning positive definite continued fractions

J. S. MacNerney; 663-677

Inequalities among some real modular functions

Peter Flor; 679-682

The denseness of the extreme points of the generalized resolvents of a symmetric operator

Richard C. Gilbert; 683-691

The composition of graphs

Gert Sabidussi; 693-696

Correction to “Kernel functions and eigenfunction expansions”

Edward Nelson; 697-698

On fiber homotopy equivalence

Errata: “The square root set of a simple basic set of polynomials, vol. 25 (1958), pp. 177–180

M. N. Mikhail; 707

Errata: Polynomial $3$-cocycles over fields of characteristic $p$,” vol. 26 (1959), pp. 269–275

Robert Heaton; 707

Errata: “An extension of E. Hopf’s maximum principle with an application to Riemannian geometry,” vol. 25 (1958), pp. 45–56

E. Calabi; 707

Errata: “Bernoulli and Euler numbers and orthogonal polynomials,” vol. 26 (1959), pp. 1–15

L. Carlitz; 707