Variational Methods for Eigenvalue Problems : : An Introduction to the Weinstein Method of Intermediate Problems (Second Edition) / / S. H. Gould.

• Superior document: Title is part of eBook package: De Gruyter University of Toronto Press eBook-Package Archive 1933-1999
• VerfasserIn: Gould, S. H.,
• Place / Publishing House: Toronto : : University of Toronto Press, , [2019]; ©1966
• Year of Publication: 2019
• Edition: 2nd Edition
• Language: English
• Series: Heritage
• Physical Description: 1 online resource (292 p.)

The first edition of this book gave a systematic exposition of the Weinstein method of calculating lower bounds of eigenvalues by means of intermediate problems. From the reviews of this edition and from subsequent shorter expositions it has become clear that the method is of considerable interest to the mathematical world; this interest has increased greatly in recent years by the success of some mathematicians in simplifying and extending the numerical applications, particularly in quantum mechanics. Until now new developments have been available only in articles scattered throughout the literature: this second edition presents them systematically in the framework of the material contained in the first edition, which is retained in somewhat modified form.

Table of Contents

Frontmatter -- PREFACE TO THE SECOND EDITION -- FROM THE PREFACE TO THE FIRST EDITION -- CONTENTS -- INTRODUCTION -- I. SYSTEMS VIBRATING WITH A FINITE NUMBER OF DEGREES OF FREEDOM -- II. VARIATIONAL PRINCIPLES FOR FINITE-DIMENSIONAL SYSTEMS -- III. THE WEINSTEIN CRITERION FOR COMPLETE RAISING OF EIGENVALUES -- IV. VIBRATION OF SYSTEMS WITH INFINITELY MANY DEGREES OF FREEDOM -- V. REPRODUCING KERNELS AND FUNCTIONAL COMPLETION -- VI. VIBRATING RODS, MEMBRANES, AND PLATES -- VII. THE WEINSTEIN METHOD IN ITS ORIGINAL FORM -- VIII. LINEAR OPERATORS IN HILBERT SPACE -- IX. THE METHOD AS DEVELOPED BY WEINSTEIN AND ARONSZAJN FOR LINEAR OPERATORS IN HILBERT SPACE -- X. APPLICATION OF THE METHOD IN HILBERT SPACE TO THE DIFFERENTIAL PROBLEM OF THE VIBRATING PLATE -- XI. APPLICATION OF THE APPROXIMATIVE METHODS TO GENERAL DIFFERENTIAL PROBLEMS -- XII. INTERMEDIATE PROBLEMS OF THE SECOND TYPE. THE BAZLEY SPECIAL CHOICE -- XIII. TRUNCATION AND OTHER METHODS -- XIV. PROBLEMS OF THE FIRST TYPE WITH A SIDE CONDITION -- XV. UNIFIED TREATMENT OF INTERMEDIATE PROBLEMS -- BIBLIOGRAPHY -- INDEX