Elements of Hilbert Spaces and Operator Theory. 1st ed. 2017

種類:

電子ブック

責任表示:

by Harkrishan Lal Vasudeva

出版情報:

Singapore : Springer Nature Singapore : Imprint: Springer, 2017

著者名:

• Vasudeva, Harkrishan Lal.
• SpringerLink (Online service)

ISBN:

9789811030208 [9811030200]    

注記:

Preface -- Preliminaries -- Inner Product Spaces -- Linear Operators -- Spectral Theory and Special Classes of Operators -- Banach Spaces -- Hints and Solutions -- References -- Index. .
The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compressio

ローカル注記:

岐阜大学構成員専用E-BOOKS (Gifu University members only)