Elements of Hilbert Spaces and Operator Theory

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Mathematical Analysis
Cover of the book Elements of Hilbert Spaces and Operator Theory by Harkrishan Lal Vasudeva, Springer Singapore
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Harkrishan Lal Vasudeva ISBN: 9789811030208
Publisher: Springer Singapore Publication: March 27, 2017
Imprint: Springer Language: English
Author: Harkrishan Lal Vasudeva
ISBN: 9789811030208
Publisher: Springer Singapore
Publication: March 27, 2017
Imprint: Springer
Language: English

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 compression spectrum, have been worked out. Spectral theorems for self-adjoint operators, and normal operators, follow the spectral theorem for compact normal operators. The book also discusses invariant subspaces with special attention to the Volterra operator and unbounded operators.

In order to make the text as accessible as possible, motivation for the topics is introduced and a greater amount of explanation than is usually found in standard texts on the subject is provided. The abstract theory in the book is supplemented with concrete examples. It is expected that these features will help the reader get a good grasp of the topics discussed. Hints and solutions to all the problems are collected at the end of the book. Additional features are introduced in the book when it becomes imperative. This spirit is kept alive throughout the book.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 compression spectrum, have been worked out. Spectral theorems for self-adjoint operators, and normal operators, follow the spectral theorem for compact normal operators. The book also discusses invariant subspaces with special attention to the Volterra operator and unbounded operators.

In order to make the text as accessible as possible, motivation for the topics is introduced and a greater amount of explanation than is usually found in standard texts on the subject is provided. The abstract theory in the book is supplemented with concrete examples. It is expected that these features will help the reader get a good grasp of the topics discussed. Hints and solutions to all the problems are collected at the end of the book. Additional features are introduced in the book when it becomes imperative. This spirit is kept alive throughout the book.

More books from Springer Singapore

Cover of the book The Challenge of Reframing Engineering Education by Harkrishan Lal Vasudeva
Cover of the book Mathematics and Computing by Harkrishan Lal Vasudeva
Cover of the book Automorphisms of Finite Groups by Harkrishan Lal Vasudeva
Cover of the book Chinese Business by Harkrishan Lal Vasudeva
Cover of the book Regeneration of Peasants by Harkrishan Lal Vasudeva
Cover of the book Alloys and Composites of Polybenzoxazines by Harkrishan Lal Vasudeva
Cover of the book General Purpose Technology, Spin-Out, and Innovation by Harkrishan Lal Vasudeva
Cover of the book Re-visioning the Public in Post-reform Urban China by Harkrishan Lal Vasudeva
Cover of the book Production of Materials from Sustainable Biomass Resources by Harkrishan Lal Vasudeva
Cover of the book The Six-Party Talks on North Korea by Harkrishan Lal Vasudeva
Cover of the book Computational Ship Design by Harkrishan Lal Vasudeva
Cover of the book Metabolic Engineering for Bioactive Compounds by Harkrishan Lal Vasudeva
Cover of the book Environmental Biotechnology: For Sustainable Future by Harkrishan Lal Vasudeva
Cover of the book Impact of Food Processing on Anthocyanins by Harkrishan Lal Vasudeva
Cover of the book Chinese Education Models in a Global Age by Harkrishan Lal Vasudeva
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy