Introduction to Spectral Theory, P.D. Hislop; I.M. Sigal

Автор: Hislop
Название: Introduction to Spectral Theory
ISBN: 0387945016 ISBN-13(EAN): 9780387945019
Издательство: Springer
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Цена: 23757.00 р.
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Описание: This work aims to introduce students to active areas of research in mathematical physics in a rather direct way, thus minimizing the use of abstract mathematics. The book`s main features are geometric methods in spectral analysis, semi-classical analysis of resonance and other topics.

Автор: Motohashi
Название: Spectral Theory of the Riemann Zeta-Function
ISBN: 0521058074 ISBN-13(EAN): 9780521058070
Издательство: Cambridge Academ
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Описание: Professor Motohashi shows that the Riemann zeta function is closely bound with automorphic forms and that many results from there can be woven with techniques and ideas from analytic number theory to yield new insights into, and views of, the function itself.

Автор: Jan Janas; Pavel Kurasov; A. Laptev; Sergei Naboko
Название: Spectral Theory and Analysis
ISBN: 3034803265 ISBN-13(EAN): 9783034803267
Издательство: Springer
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Цена: 16070.00 р.
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Описание: This volume contains the proceedings of the OTAMP 2008 (Operator Theory, Analysis and Mathematical Physics) conference held at the Mathematical Research and Conference Center in Bedlewo near Poznan.

Автор: Borthwick
Название: Spectral Theory of Infinite-Area Hyperbolic Surfaces
ISBN: 3319338757 ISBN-13(EAN): 9783319338750
Издательство: Springer
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Цена: 15372.00 р.
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Описание: This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural setting for development of the spectral theory while still keeping technical difficulties to a minimum. All of the material from the first edition is included and updated, and new sections have been added.Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson-Sullivan theory, and the dynamical approach to the zeta function. The new sections cover the latest developments in the field, including the spectral gap, resonance asymptotics near the critical line, and sharp geometric constants for resonance bounds. A new chapter introduces recently developed techniques for resonance calculation that illuminate the existing results and conjectures on resonance distribution.The spectral theory of hyperbolic surfaces is a point of intersection for a great variety of areas, including quantum physics, discrete groups, differential geometry, number theory, complex analysis, and ergodic theory. This book will serve as a valuable resource for graduate students and researchers from these and other related fields. Review of the first edition:'The exposition is very clear and thorough, and essentially self-contained; the proofs are detailed...The book gathers together some material which is not always easily available in the literature...To conclude, the book is certainly at a level accessible to graduate students and researchers from a rather large range of fields. Clearly, the reader...would certainly benefit greatly from it.' (Colin Guillarmou, Mathematical Reviews, Issue 2008 h)

Автор: Bertrand Mercier
Название: An Introduction to the Numerical Analysis of Spectral Methods
ISBN: 3662137577 ISBN-13(EAN): 9783662137574
Издательство: Springer
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Цена: 11753.00 р.
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Описание: This is a very lucid introduction to spectral methods emphasizing the mathematical aspects of the theory rather than the many applications in numerical analysis and the engineering sciences. The first part is a fairly complete introduction to Fourier series while the second emphasizes polynomial expansion methods like Chebyshev`s.