Variational Methods for Eigenvalue Problems: An Introduction to the Weinstein Method of Intermediate Problems (Second Edition)

✍ Scribed by S. H. Gould

• Publisher: University of Toronto Press
• Year: 1966
• Tongue: English
• Leaves: 291
• Edition: 2
• Category: Library

✦ Synopsis

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. This second edition presents new developments in the framework of the material contained in the first edition, which is retained in somewhat modified form.

✦ Table of Contents

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