This volume, published on the occasion of his 75th birthday, contains sixty original papers by leading mathematicians of the United States and Europe who have been inspired by the teaching or researches of Professor Polya, together with a list of Polya's publications and a preface by the editors on his distinguished career. Most of the papers are in fields to which P61ya himself has contributed, and many of the authors indicate Polya's influence on the development of their subjects and give fuller historical backgrounds than are usual in research papers. Predictably one finds the names of Boas, Erdelyi, Hayman, Littlewood, Szego, Titchmarsh, Zygmund and others in the list of authors, but the presence of such names as Brauer, Coxeter and Davenport is a striking reminder of the breadth of Polya's interests and his contributions to pure and applied mathematics. It was not to be expected that every one of the authors could produce a specimen of his most memorable work to order for the occasion, but this well-produced volume is a worthy tribute to one of the most outstanding mathematicians of our time.
P. HEYWOOD, Proceedings of the Edinburgh Mathematical Society, 14(1) 1964 , p.82.
Author(s): Gábor Szegö; Charles Loewner; Stefan Bergman; Menahem Max Schiffer; Jerzy Neyman; David Gilbarg; Herbert Solomon; George Pólya
Publisher: Stanford University Press
Year: 1962
Language: English
Pages: 447
City: Stanford, California
Preface
Contents
Publications of George Polya
Geodesic Curvature and Area. Lars V. Ahlfors
Reciprocity Theorem in Cyclotomic Fields. N. C. Ankeny
Uber abstrakte und konkrete Riemannflichen. Heinrich Behnke und Giinter Scheja
On Value Distribution of Meromorphic Functions of Two Complex Variables. Stefan Bergman
On Additive Functions of a Positive Integer. A. S . Besicovitch
Inequalities for Polynomials with a Prescribed Zero. R. P. Boas, Jr.
On the Theorems of Perron and Frobenius on Non-negative Matrices. Alfred Brauer
On Some Conjectures Concerning Finite Simple Groups. Richard Brauer
The Total Length of the Edges of a Non-Euclidian Polyhedron. H. S . M. Coxeter
On the Approximation to a Stable Probability Distribution. Harald Cramér
A Note on Diophantine Approximation. H. Davenport
Generalized Means. B . Eckmann, T. Ganea, and P. J. Hilton
Meromorphic Functions with Values that Are Both Deficient and Asymptotic. Albert Edrei
A Result on Non-linear Volterra Integral Equations. A. Erdélyi
On a Problem of A. Zygmund. P. Erdés and A. Rényi
An Entire Function with Assigned Deficiencies. W.H. Fuchs and W. K. Hayman
Proof of Uniqueness by Symmetrization. P. R. Garabedian
Vollstindig stetige Umwendung ebener Eibereiche im Raum. H. Hadwiger
Contribution to the Method of Interior Parallels Applied to Vibrating Membranes. Joseph Hersch
Remarks on Differential Equations in Banach Algebras. Einar Hille
Probabilities of Rankings for Two Widely Separated Normal Distributions. J. L . Hodges, Jr. and E. L . Lehmann
Ein raumliches Analogon des Wiman-Heinsschen Satzes. Alfred Huber
On Absolutely Convergent Dirichlet Series. 4. E . Ingham
Statistical Mechanics of Some One-Dimensional Systems. M . Kac
On the Distribution of Intersections of Diagonals in Regular Polygons. J. Karamata
On Some Classes of Functions Associated with Exponential Polynomials. Samuel Karlin and Charles Loewner
Limits of Polynomials with Restricted Zeros. J. Korecvaar
An Integral Approach to the Calculus of Variations. C. Lanczos
A Procedure for Obtaining Upper Bounds for the Eigenvalues of a Hermitian Symmetric Operator. Peter D. Lax
Heuristics, Anyone? D. H. Lehmer and Emma Lehmer
Remarques sur un Probleme Relatif aux Lois Stables. Paul Lévy
On the Real Roots of Real Trigonometrical Polynomials. J. E . Littlewood
On the Principal Frequency of a Membrane and the Torsional Rigidity of a Beam. E . Makai
Dirichlet Series. S . Mandelbrojt
On Some Aspects of Non-linear Oscillations. N . Minorsky
On an Inequality of Lyapunov. Zeev Nehari
Contribution to the Study of the Abundance of Multiple Galaxies. Jerzy Neyman and Elizabeth L. Scott
Some Isoperimetric Inequalities in the Torsion Problem for Multiply Connected Regions. L . E. Payne
Le Probléme d’Itération Posé par Certaines Lois d’Impéts. M. Plancherel
On Multiplicative Arithmetic Functions. J . Popken
On a Theorem of Besicovitch. Hans Rademacher
On the Decision Problem for Algebraic Rings. Julia Robinson
Intervals Containing Infinitely Many Sets of Conjugate Algebraic Integers. Raphael M. Robinson
Non-negative Linear Functionals, Moment Problems, and Extremum Problems in Polynomial Spaces. W. W . Rogosinski
Probability and Entire Functions. P. C . Rosenbloom
The Growth of a Fundamental Solution of an Elliptic Divergence Structure Equation. H. L . Royden
Transfinite Diameter and Analytic Continuation of Functions of Two Complex Variables. M. Schiffer and J. Siciak
On the Besicovitch-Perron Solution of the Kakeya Problem. I. J . Schoenberg
Convergence de Distributions dont les Dérivées Convergent. Laurent Schwartz
Intrinsic Formulation of the Equation of Structure of a Transitive Continuous Pseudogroup. D. C . Spencer
On the Form of Complete Surfaces in Three-Dimensional Space for which K<=-c^2 or K>=c^2. J.J.Stoker
On the Proofs of the Fundamental Theorem of Number Theory. Janos Surdnyi
An Inequality for Jacobi Polynomials. Gabor Szego
On an Eigenvalue Problem Occurring in Quantum Mechanics. E. C. Titchmarsh
On a Certain Problem in the Theory of Power Series with Gaps. P. Turan
Can a Series Possess a Sum 1 and an Asymptotic Sum 0? J. G. Van der Corput
On the Convexity of the Ovals of Lemniscates. J. L . Walsh
Symmetrization in Uniformly Elliptic Problems. H. F. Weinberger
A Necessary and Sufficient Condition in the Maximum-Minimum Theory of Eigenvalues. A. Weinstein
On One-Sided Localization of Trigonometric Series. A. Zygmund
