Commuting Nonselfadjoint Operators in Hilbert Space, Moshe S. Livsic; Leonid L. Waksman

Автор: Schm?dgen
Название: Unbounded Self-Adjoint Operators on Hilbert Space
ISBN: 9400747527 ISBN-13(EAN): 9789400747524
Издательство: Springer
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Описание: The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schroedinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) .

Автор: Kurt O. Friedrichs
Название: Spectral Theory of Operators in Hilbert Space
ISBN: 0387900764 ISBN-13(EAN): 9780387900766
Издательство: Springer
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Описание: The present lectures intend to provide an introduction to the spectral analysis of self-adjoint operators within the framework of Hilbert space theory. Next, simple differential operators are treated as operators in Hilbert space, and the final chapter deals with the perturbation of discrete and continuous spectra.

Автор: Jir? Blank; Pavel Exner; Miloslav Havl?cek
Название: Hilbert Space Operators in Quantum Physics
ISBN: 9048180120 ISBN-13(EAN): 9789048180127
Издательство: Springer
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Описание: The new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.

Автор: P. de la Harpe
Название: Classical Banach-Lie Algebras and Banach-Lie Groups of Operators in Hilbert Space
ISBN: 3540059849 ISBN-13(EAN): 9783540059844
Издательство: Springer
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Автор: Calvin R. Putnam
Название: Commutation Properties of Hilbert Space Operators and Related Topics
ISBN: 3642859402 ISBN-13(EAN): 9783642859403
Издательство: Springer
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Автор: Ruben A. Martinez-Avendano; Peter Rosenthal
Название: An Introduction to Operators on the Hardy-Hilbert Space
ISBN: 1441922539 ISBN-13(EAN): 9781441922533
Издательство: Springer
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Цена: 7685.00 р.
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Описание: The great mathematician G. H. Hardy told us that "Beauty is the ?rst test: there is no permanent place in the world for ugly mathematics" (see 24, p. 85]). It is clear why Hardy loved complex analysis: it is a very beautiful partofclassicalmathematics. ThetheoryofHilbertspacesandofoperatorson themisalmostasclassicalandisperhapsasbeautifulascomplexanalysis. The studyoftheHardy-Hilbertspace(aHilbertspacewhoseelementsareanalytic functions), and of operators on that space, combines these two subjects. The interplay produces a number of extraordinarily elegant results. For example, very elementary concepts from Hilbert space provide simple proofs of the Poisson integral (Theorem 1. 1. 21 below) and Cauchy integral (Theorem 1. 1. 19) formulas. The fundamental theorem about zeros of fu- tions in the Hardy-Hilbert space (Corollary 2. 4. 10) is the central ingredient of a beautiful proof that every continuous function on 0,1] can be uniformly approximated by polynomials with prime exponents (Corollary 2. 5. 3). The Hardy-Hilbert space context is necessary to understand the structure of the invariant subspaces of the unilateral shift (Theorem 2. 2. 12). Conversely, pr- erties of the unilateral shift operator are useful in obtaining results on f- torizations of analytic functions (e. g., Theorem 2. 3. 4) and on other aspects of analytic functions (e. g., Theorem 2. 3. 3). The study of Toeplitz operators on the Hardy-Hilbert space is the most natural way of deriving many of the properties of classical Toeplitz mat- ces (e. g., Theorem 3. 3.

Автор: M.S. Livsic; N. Kravitsky; A.S. Markus; V. Vinniko
Название: Theory of Commuting Nonselfadjoint Operators
ISBN: 9048145856 ISBN-13(EAN): 9789048145850
Издательство: Springer
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Цена: 30467.00 р.
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Автор: Jir? Blank; Pavel Exner; Miloslav Havl?cek
Название: Hilbert Space Operators in Quantum Physics
ISBN: 1402088698 ISBN-13(EAN): 9781402088698
Издательство: Springer
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Цена: 15372.00 р.
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Описание: Explains the theory of linear Hilbert-space operators and their use in quantum physics. This book focuses on the spectral theory of self-adjoint operators. It discusses logical building of the operator structure of quantum theory as well as its practical aspects, such as spectral properties of quantum mechanical Hamiltonians and scattering theory.

Автор: J.M. Bachar; D.W. Hadwin
Название: Hilbert Space Operators
ISBN: 3540090975 ISBN-13(EAN): 9783540090977
Издательство: Springer
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Автор: Sheldon Axler; Peter Rosenthal; Donald Sarason
Название: A Glimpse at Hilbert Space Operators
ISBN: 3034803109 ISBN-13(EAN): 9783034803106
Издательство: Springer
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Цена: 13974.00 р.
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Описание: This commemorative volume honors mathematician Paul R. Halmos, whose research, unparalleled mathematical exposition, and dedication to service made a major impact on the mathematics community. Various articles discuss his contributions to the operator theory.

Автор: M.S. Livsic; N. Kravitsky; A.S. Markus; V. Vinniko
Название: Theory of Commuting Nonselfadjoint Operators
ISBN: 0792335880 ISBN-13(EAN): 9780792335887
Издательство: Springer
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Описание: Proposing a rigorous mathematical definition of the physical concept of a particle, this book obtains a concrete image of a particle conceived as a localised entity in space. It is intended for researchers and postgraduate students in operator theory, system theory, quantum physics and algebraic geometry.

Автор: A. Feintuch; I. Gohberg
Название: Nonselfadjoint Operators and Related Topics
ISBN: 3034896638 ISBN-13(EAN): 9783034896634
Издательство: Springer
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Описание: Our goal is to find Grabner bases for polynomials in four different sets of expressions: 1 x-, (1 - x)-1 (RESOL) X, 1 x- (1 - xy)-1 (EB) X, y-1, (1-yx)-1 y, (1_y)-1 (1-x)-1 (preNF) (EB) plus and (1 - xy)1/2 (1 - yx )1/2 (NF) (preNF) plus and Most formulas in the theory of the Nagy-Foias operator model NF] are polynomials in these expressions where x = T and y = T*. Complicated polynomials can often be simplified by applying "replacement rules". For example, the polynomial (1 - xy)-2 - 2xy(1-xy)-2 + xy2 (1 - xy)-2 -1 simplifies to O. This can be seen by three applications of the replacement rule (1-xy) -1 xy -t (1 - xy)-1 -1 which is true because of the definition of (1-xy)-1. A replacement rule consists of a left hand side (LHS) and a right hand side (RHS). The LHS will always be a monomial. The RHS will be a polynomial whose terms are "simpler" (in a sense to be made precise) than the LHS. An expression is reduced by repeatedly replacing any occurrence of a LHS by the corresponding RHS. The monomials will be well-ordered, so the reduction procedure will terminate after finitely many steps. Our aim is to provide a list of substitution rules for the classes of expressions above. These rules, when implemented on a computer, provide an efficient automatic simplification process. We discuss and define the ordering on monomials later.