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Author: Jussi Behrndt
Publisher: Springer Science & Business Media
ISBN: 3764389117
Category : Mathematics
Languages : en
Pages : 261
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Book Description
Contains a collection of research papers originating from the 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, which was held at the TU Berlin, Germany, December 14 to 17. This work discusses topics such as linear relations, singular perturbations, de Branges spaces, nonnegative matrices, and abstract kinetic equations.
Author: Jussi Behrndt
Publisher: Springer Science & Business Media
ISBN: 3764389117
Category : Mathematics
Languages : en
Pages : 261
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Book Description
Contains a collection of research papers originating from the 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, which was held at the TU Berlin, Germany, December 14 to 17. This work discusses topics such as linear relations, singular perturbations, de Branges spaces, nonnegative matrices, and abstract kinetic equations.
Author: Andrei Giniatoulline
Publisher: R.T. Edwards, Inc.
ISBN: 9781930217096
Category : Mathematics
Languages : en
Pages : 212
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Book Description
A brief and accessible introduction to the spectral theory of linear second order elliptic differential operators. By introducing vital topics of abstract functional analysis where necessary, and using clear and simple proofs, the book develops an elegant presentation of the theory while integrating applications of basic real world problems involving the Laplacian. Suitable for use as a self-contained introduction for beginners or as a one-semester student text; contains some 25 examples and 60 exercises, most with detailed hints.
Author: P.D. Hislop
Publisher: Springer
ISBN: 9781461268888
Category : Technology & Engineering
Languages : en
Pages : 0
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Book Description
The intention of this book is to introduce students to active areas of research in mathematical physics in a rather direct way minimizing the use of abstract mathematics. The main features are geometric methods in spectral analysis, exponential decay of eigenfunctions, semi-classical analysis of bound state problems, and semi-classical analysis of resonance. A new geometric point of view along with new techniques are brought out in this book which have both been discovered within the past decade. This book is designed to be used as a textbook, unlike the competitors which are either too fundamental in their approach or are too abstract in nature to be considered as texts. The authors' text fills a gap in the marketplace.
Author: Michael Sh. Birman
Publisher: Springer Science & Business Media
ISBN: 9400945868
Category : Mathematics
Languages : en
Pages : 316
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Book Description
It isn't that they can't see the solution. It is Approach your problems from the right end that they can't see the problem. and begin with the answers. Then one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be com pletely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order" , which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Author: Kurt Otto Friedrichs
Publisher:
ISBN: 9781258444051
Category :
Languages : en
Pages : 218
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Book Description
The Present Lectures Intend To Provide An Introduction To The Spectral Analysis Of Self-Joint Operators Within The Framework Of Hilbert Space Theory. The Guiding Notion In This Approach Is That Of Spectral Representation. At The Same Time The Notion Of Function Of An Operator Is Emphasized. The Definition Of Hilbert Space: In Mathematics, A Hilbert Space Is A Real Or Complex Vector Space With A Positive-Definite Hermitian Form, That Is Complete Under Its Norm. Thus It Is An Inner Product Space, Which Means That It Has Notions Of Distance And Of Angle (Especially The Notion Of Orthogonality Or Perpendicularity). The Completeness Requirement Ensures That For Infinite Dimensional Hilbert Spaces The Limits Exist When Expected, Which Facilitates Various Definitions From Calculus. A Typical Example Of A Hilbert Space Is The Space Of Square Summable Sequences. Hilbert Spaces Allow Simple Geometric Concepts, Like Projection And Change Of Basis To Be Applied To Infinite Dimensional Spaces, Such As Function Spaces. They Provide A Context With Which To Formalize And Generalize The Concepts Of The Fourier Series In Terms Of Arbitrary Orthogonal Polynomials And Of The Fourier Transform, Which Are Central Concepts From Functional Analysis. Hilbert Spaces Are Of Crucial Importance In The Mathematical Formulation Of Quantum Mechanics.
Author: Simone Malacrida
Publisher: Simone Malacrida
ISBN:
Category : Mathematics
Languages : en
Pages : 52
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Book Description
The following topics are presented in this book: basic concepts of operator functional analysis spectral theorem and spectral measurements Stone's theorem and physical applications
Author: Pietro Aiena
Publisher: Springer Science & Business Media
ISBN: 1402025254
Category : Mathematics
Languages : en
Pages : 452
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Book Description
A signi?cant sector of the development of spectral theory outside the classical area of Hilbert space may be found amongst at multipliers de?ned on a complex commutative Banach algebra A. Although the general theory of multipliers for abstract Banach algebras has been widely investigated by several authors, it is surprising how rarely various aspects of the spectral theory, for instance Fredholm theory and Riesz theory, of these important classes of operators have been studied. This scarce consideration is even more surprising when one observes that the various aspects of spectral t- ory mentioned above are quite similar to those of a normal operator de?ned on a complex Hilbert space. In the last ten years the knowledge of the spectral properties of multip- ers of Banach algebras has increased considerably, thanks to the researches undertaken by many people working in local spectral theory and Fredholm theory. This research activity recently culminated with the publication of the book of Laursen and Neumann [214], which collects almost every thing that is known about the spectral theory of multipliers.
Author: K. B. Laursen
Publisher: Oxford University Press
ISBN: 9780198523819
Category : Mathematics
Languages : en
Pages : 610
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Book Description
Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces. This book provides an in-depth introduction to the natural expansion of this fascinating topic of Banach space operator theory. It gives complete coverage of the field, including the fundamental recent work by Albrecht and Eschmeier which provides the full duality theory for Banach space operators. One of its highlights are the many characterizations of decomposable operators, and of other related, important classes of operators, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity. Written in a careful and detailed style, it contains numerous examples, many simplified proofs of classical results, extensive references, and open problems, suitable for continued research.
Author: Gilbert Helmberg
Publisher:
ISBN:
Category : Hilbert space
Languages : en
Pages : 368
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Book Description
Author: Nakano Hidegoro
Publisher: Legare Street Press
ISBN: 9781018612010
Category :
Languages : en
Pages : 0
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Book Description
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
