Author: E. J. Specht
Publisher:
ISBN:
Category : Hilbert space
Languages : en
Pages : 104

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Book Description

Author: Harold Trainer Jones
Publisher:
ISBN:
Category :
Languages : en
Pages : 138

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Book Description

Author: E. J. Specht
Publisher:
ISBN:
Category : Hilbert space
Languages : en
Pages : 92

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Book Description

Author: N. I. Akhiezer
Publisher: Courier Corporation
ISBN: 0486318656
Category : Mathematics
Languages : en
Pages : 378

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Book Description
This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.

Author: Joachim Weidmann
Publisher: Springer Science & Business Media
ISBN: 1461260272
Category : Mathematics
Languages : en
Pages : 413

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Book Description
This English edition is almost identical to the German original Lineare Operatoren in Hilbertriiumen, published by B. G. Teubner, Stuttgart in 1976. A few proofs have been simplified, some additional exercises have been included, and a small number of new results has been added (e.g., Theorem 11.11 and Theorem 11.23). In addition a great number of minor errors has been corrected. Frankfurt, January 1980 J. Weidmann vii Preface to the German edition The purpose of this book is to give an introduction to the theory of linear operators on Hilbert spaces and then to proceed to the interesting applica tions of differential operators to mathematical physics. Besides the usual introductory courses common to both mathematicians and physicists, only a fundamental knowledge of complex analysis and of ordinary differential equations is assumed. The most important results of Lebesgue integration theory, to the extent that they are used in this book, are compiled with complete proofs in Appendix A. I hope therefore that students from the fourth semester on will be able to read this book without major difficulty. However, it might also be of some interest and use to the teaching and research mathematician or physicist, since among other things it makes easily accessible several new results of the spectral theory of differential operators.

Author: Harkrishan Lal Vasudeva
Publisher: Springer
ISBN: 9811030200
Category : Mathematics
Languages : en
Pages : 528

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Book Description
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.

Author: Israel Gohberg
Publisher: American Mathematical Soc.
ISBN: 9780821886502
Category : Mathematics
Languages : en
Pages : 402

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Book Description

Author: Naum Il'ič Ahiezer
Publisher:
ISBN:
Category :
Languages : en
Pages : 218

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Book Description

Author: Naum Ilʹich Akhiezer
Publisher: Courier Dover Publications
ISBN: 9780486677484
Category : Mathematics
Languages : en
Pages : 404

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Book Description
One of the classic textbooks in the field, this outstanding work introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators.

Author: Israel Gohberg
Publisher: American Mathematical Soc.
ISBN: 9780821886540
Category : Mathematics
Languages : en
Pages : 444

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Book Description
An abstract Volterra operator is, roughly speaking, a compact operator in a Hilbert space whose spectrum consists of a single point $\lambda=0$. The theory of abstract Volterra operators, significantly developed by the authors of the book and their collaborators, represents an important part of the general theory of non-self-adjoint operators in Hilbert spaces. The book, intended for all mathematicians interested in functional analysis and its applications, discusses the main ideas and results of the theory of abstract Volterra operators. Of particular interest to analysts and specialists in differential equations are the results about analytic models of abstract Volterra operators and applications to boundary value problems for ordinary differential equations.