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TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

EDITED BY

A. A. ALBERT OSCAR ZARISKI ANTONI ZYGMUND

WITH THE COOPERATION OF

RICHARD BRAUER NELSON DUNFORD SAMUEL EILENBERG WILLIAM FELLER G. A. HEDLUND NATHAN JACOBSON IRVING KAPLANSKY S. C. KLEENE M. S. KNEBELMAN HARRY LEVY SAUNDERS MacLANE C. B. MORREY W. T. REID O. F. G. SCHILLING N. E. STEENROD J. J. STOKER D. J. STRUIK HASSLER WHITNEY R. L. WILDER

VOLUME 63 JANUARY TO JUNE 1948

PUBLISHED BY THE SOCIETY MENASHA, WIS., AND NEW YORK 1948

Reprinted with the permission of The American Mathematical Society

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PRINTED IN THE UNITED STATES OF AMERICA TABLE OF CONTENTS VOLUME 63, JANUARY TO JUNE, 1948

Arens, R. F., and Kaplansky, I. Topological representation of algebras. . 457

Bergman, S. Functions of extended class in the theory of functions of several complex variables. 523

Bergman, S. Errata for Two-dimensional subsonic flows of a com- pressible fluid and their singularities. 599

Carruth, P. W. Generalized power series fields. 548

Chevalley, C, and Eilenberg, S. Cohomology theory of Lie groups and Lie algebras. 85

Doob, J. L. Asymptotic properties of Markoff transition probabilities. . 393

Doob, J. L. Renewal theory from the point of view of the theory of probability. 422

Eilenberg, S., and Chevalley, C. Cohomology theory of Lie groups and Lie algebras. 85

Godement, R. Les fonctions de type positif et la théorie des groupes.. 1 Good, R. A. On the theory of clusters. 482

Goodman, A. W. On some determinants related to p-valent functions. 175 Greenstone, L. Mapping by analytic functions: Part I. Conformai mapping of multiply-connected domains.125, 600

Hartman, P. Unrestricted solution fields of almost-separable differen- tial equations. 560

Hartman, P., and Wintner, A. Töplerian (L2)-bases. 207

Horn, A. The asymptotic behavior of solutions of systems of Volterra integral equations. 144

Jackson, D. The boundedness of orthonormal polynomials on certain curves of the fourth degree. 193

Kac, M., Salem R., and Zygmund, A. A gap theorem. 235 Kaplan, W. Topology of level curves of harmonic functions. 514 Kaplansky, I., and Arens, R. F. Topological representation of algebras 457

Karush, W. A semi-strong minimum for a multiple integral problem in the calculus of variations. 439 Lorentz, G. G. Tauberian theorems and Tauberian conditions. 226

Mickle, E. J. Metric foundations of continuous transformations.. . . 368 Moïse, E. E. An indecomposible plane continuum which is homeo- morphic to each of its nondegenerate subcontinua. 581 Pollard, H. The mean convergence of orthogonal series, II. 355 Protter, M. H. Generalized spherical harmonics. 314

Salem, R. Rectifications to the papers Sets of uniqueness and sets of multiplicités. I, II. 595 Salem R., Zygmund, A., and Kac, M. A gap theorem. 235 Sheffer, I. M. On ¿-periodic systems of linear equations. 244 Su, B. Errata for Descriptive collineations in spaces of A-spreads. . .. 599

Weinstein, A. Discontinuous integrals and generalized potential theory. 342 Whyburn, G. T. On n-arc connectedness. 452 Wintner, A., and Hartman, P. Töplerian (Z,2)-bases. 207 Zygmund, A., Kac, M., and Salem, R. A gap theorem. 235