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Book DetailsAmerican Mathematical Society Translations - Series 2Advances in the Mathematical SciencesVolume: 233; 2014; 251 ppMSC: Primary 34; 35; 47; 60; 81
This volume is dedicated to V. A. Marchenko on the occasion of his 90th birthday. It contains refereed original papers and survey articles written by his colleagues and former students of international stature and focuses on the areas to which he made important contributions: spectral theory of differential and difference operators and related topics of mathematical physics, including inverse problems of spectral theory, homogenization theory, and the theory of integrable systems. The papers in the volume provide a comprehensive account of many of the most significant recent developments in that broad spectrum of areas.
ReadershipResearch mathematicians interested in spectral theory and differential operators and their applications.
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Table of Contents
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Chapters
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V. M. Adamyan, G. J. Martin and B. S. Pavlov — Local inverse scattering problem as a tool of perturbation analysis for resonance systems
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Hans-Dieter Alber — The continuous theory of dislocations for a material containing dislocations to one Burgers vector only
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A. I. Aptekarev — Spectral problems of high-order recurrences
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Anne Boutet de Monvel, Igor Loutsenko and Oksana Yermolayeva — On the multi-fractal spectrum of the whole-plane Lévy-Loewner evolution
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Anne Boutet de Monvel and Lech Zielinski — Asymptotic behavior of large eigenvalues of a modified Jaynes-Cummings model
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S. Yu. Dobrokhotov, G. Makrakis and V. E. Nazaikinskii — Fourier integrals and a new representation of Maslov’s canonical operator near caustics
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Jonathan Eckhardt, Aleksey Kostenko and Gerald Teschl — Inverse uniqueness results for one-dimensional weighted Dirac operators
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Alexandre Eremenko and Andrei Gabrielov — Spectral loci of Sturm-Liouville operators with polynomial potentials
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Olivier Guédon, Anna Lytova, Alain Pajor and Leonid Pastur — The central limit theorem for linear eigenvalue statistics of the sum of independent random matrices of rank one
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T. Kappeler, P. Lohrmann and P. Topalov — On the spectrum of nonself-adjoint Zakharov-Shabat operators on $\mathbb {R}$
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E. Ya. Khruslov, M. V. Goncharenko and N. K. Radyakin — Homogenized model of oscillations of elastic medium with small caverns filled with viscous incompressible fluid
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V. Yu. Novokshenov and A. A. Shchelkonogov — Double scaling limit in the Painlevé IV equation and asymptotics of the Okamoto polynomials
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A. M. Savchuk and A. A. Shkalikov — Recovering a potential of the Sturm-Liouville problem from finite sets of spectral data
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Ricardo Weder — High-velocity estimates, inverse scattering and topological effects
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Additional Material
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
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This volume is dedicated to V. A. Marchenko on the occasion of his 90th birthday. It contains refereed original papers and survey articles written by his colleagues and former students of international stature and focuses on the areas to which he made important contributions: spectral theory of differential and difference operators and related topics of mathematical physics, including inverse problems of spectral theory, homogenization theory, and the theory of integrable systems. The papers in the volume provide a comprehensive account of many of the most significant recent developments in that broad spectrum of areas.
Research mathematicians interested in spectral theory and differential operators and their applications.
-
Chapters
-
V. M. Adamyan, G. J. Martin and B. S. Pavlov — Local inverse scattering problem as a tool of perturbation analysis for resonance systems
-
Hans-Dieter Alber — The continuous theory of dislocations for a material containing dislocations to one Burgers vector only
-
A. I. Aptekarev — Spectral problems of high-order recurrences
-
Anne Boutet de Monvel, Igor Loutsenko and Oksana Yermolayeva — On the multi-fractal spectrum of the whole-plane Lévy-Loewner evolution
-
Anne Boutet de Monvel and Lech Zielinski — Asymptotic behavior of large eigenvalues of a modified Jaynes-Cummings model
-
S. Yu. Dobrokhotov, G. Makrakis and V. E. Nazaikinskii — Fourier integrals and a new representation of Maslov’s canonical operator near caustics
-
Jonathan Eckhardt, Aleksey Kostenko and Gerald Teschl — Inverse uniqueness results for one-dimensional weighted Dirac operators
-
Alexandre Eremenko and Andrei Gabrielov — Spectral loci of Sturm-Liouville operators with polynomial potentials
-
Olivier Guédon, Anna Lytova, Alain Pajor and Leonid Pastur — The central limit theorem for linear eigenvalue statistics of the sum of independent random matrices of rank one
-
T. Kappeler, P. Lohrmann and P. Topalov — On the spectrum of nonself-adjoint Zakharov-Shabat operators on $\mathbb {R}$
-
E. Ya. Khruslov, M. V. Goncharenko and N. K. Radyakin — Homogenized model of oscillations of elastic medium with small caverns filled with viscous incompressible fluid
-
V. Yu. Novokshenov and A. A. Shchelkonogov — Double scaling limit in the Painlevé IV equation and asymptotics of the Okamoto polynomials
-
A. M. Savchuk and A. A. Shkalikov — Recovering a potential of the Sturm-Liouville problem from finite sets of spectral data
-
Ricardo Weder — High-velocity estimates, inverse scattering and topological effects