Introduction to Spectral Theory in Hilbert Space

North-Holland Series in Applied Mathematics and Mechanics

Gilbert Helmberg, H. A. Lauwerier, W. T. Koiter

• Publisher: North Holland
• Year: 2014
• Print ISBN:
  9780720423563
• eBook ISBN:
  9781483164175
• Topic: Physical Sciences
• Subtopic: Mathematical & Computational Physics

North-Holland Series in Applied Mathematics and Mechanics, Volume 6: Introduction to Spectral Theory in Hilbert Space focuses on the mechanics, principles, and approaches involved in spectral theory in Hilbert space. The publication first elaborates on the concept and specific geometry of Hilbert space and bounded linear operators. Discussions focus on projection and adjoint operators, bilinear forms, bounded linear mappings, isomorphisms, orthogonal subspaces, base, subspaces, finite dimensional Euclidean space, and normed linear spaces. The text then takes a look at the general theory of linear operators and spectral analysis of compact linear operators, including spectral decomposition of a compact selfadjoint operator, weakly convergent sequences, spectrum of a compact linear operator, and eigenvalues of a linear operator. The manuscript ponders on the spectral analysis of bounded linear operators and unbounded selfadjoint operators. Topics include spectral decomposition of an unbounded selfadjoint operator and bounded normal operator, functions of a unitary operator, step functions of a bounded selfadjoint operator, polynomials in a bounded operator, and order relation for bounded selfadjoint operators. The publication is a valuable source of data for mathematicians and researchers interested in spectral theory in Hilbert space.

Table of contents

• Front Cover
• Introduction to Spectral Theory in Hilbert Space
• Copyright Page
• Table of Contents
• Dedication
• EDITORIAL NOTE
• PREFACE
• CHAPTER I. The concept of Hilbert space
• CHAPTER II. Specific geometry of Hilbert space
• CHAPTER III. Bounded linear operators
• CHAPTER IV. General theory of linear operators
• CHAPTER V. Spectral analysis of compact linear operators
• CHAPTER VI. Spectral analysis of bounded linear operators
• CHAPTER VII. Spectral analysis of unbounded selfadjoint operators
• APPENDIX A. The graph of a linear operator
• APPENDIX B. Riemann-Stieltjes and Lebesgue integration
• Bibliography
• Index of symbols
• Subject index