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X, 219 p. Hardcover. Versand aus Deutschland / We dispatch from Germany via Air Mail. Einband bestoßen, daher Mängelexemplar gestempelt, sonst sehr guter Zustand. Imperfect copy due to slightly bumped cover, apart from this in very good condition. Stamped. Progress in Mathematical Physics , Vol. 44. Sprache: Englisch.
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Verlag: Birkhäuser Boston, Birkhäuser Boston Jul 2005, 2005
ISBN 10: 0817643664 ISBN 13: 9780817643669
Sprache: Englisch
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Buch. Zustand: Neu. Neuware -Themainobjectiveofthisbookistogiveacollectionofcriteriaavailablein the spectral theory of selfadjoint operators, and to identify the spectrum and its components in the Lebesgue decomposition. Many of these criteria were published in several articles in di erent journals. We collected them, added some and gave some overview that can serve as a platform for further research activities. Spectral theory of Schr¿ odinger type operators has a long history; however the most widely used methods were limited in number. For any selfadjoint operatorA on a separable Hilbert space the spectrum is identi ed by looking atthetotalspectralmeasureassociatedwithit;oftenstudyingsuchameasure meant looking at some transform of the measure. The transforms were of the form f, (A)f which is expressible, by the spectral theorem, as (x)dµ (x) for some nite measureµ . The two most widely used functions were the sx 1 exponential function (x)=e and the inverse function (x)=(x z) . These functions are ¿usable¿ in the sense that they can be manipulated with respect to addition of operators, which is what one considers most often in the spectral theory of Schr¿ odinger type operators. Starting with this basic structure we look at the transforms of measures from which we can recover the measures and their components in Chapter 1. In Chapter 2 we repeat the standard spectral theory of selfadjoint op- ators. The spectral theorem is given also in the Hahn¿Hellinger form. Both Chapter 1 and Chapter 2 also serve to introduce a series of de nitions and notations, as they prepare the background which is necessary for the criteria in Chapter 3.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 232 pp. Englisch.
Verlag: Birkhäuser Boston, Birkhäuser Boston, 2005
ISBN 10: 0817643664 ISBN 13: 9780817643669
Sprache: Englisch
Anbieter: AHA-BUCH GmbH, Einbeck, Deutschland
Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - The spectral theory of Schrödinger operators, in particular those with random potentials, continues to be a very active field of research. This work focuses on various known criteria in the spectral theory of selfadjoint operators in order to identify the spectrum and its components a la Lebesgue decomposition.Key features and topics: Well-developed exposition of criteria that are especially useful in determining the spectra of deterministic and random Schrödinger operators occurring in quantum theory.Systematically uses measures and their transforms (Fourier, Borel, wavelet) to present a unifying theme; Establishes criteria for identifying the spectrum; Examines a series of applications to show point spectrum and continuous spectrum in some models of random operators. Presents a series of spectral-theoretic results for the perturbed operators introduced in earlier chapters with examples of localization and delocalization in the theory of disordered systems. Presents modern criteria (using wavelet transform, eigenfunction decay) that could be used to do spectral theory. Unique work in book form combining the presentation of the deterministic and random cases, which will serve as a platform for further research activities. This concise unified presentation is aimed at graduate students and researchers working in the spectral theory of Schrödinger operators with either fixed or random potentials in particular. However, given the large gap that this book fills in the literature, it will serve a wider audience of mathematical physicists because of its contribution to works in spectral theory.
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