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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.

Table of Contents

Chapters

V. M. Adamyan, G. J. Martin and B. S. Pavlov — Local inverse scattering problem as a tool of perturbation analysis for resonance systems

HansDieter Alber — The continuous theory of dislocations for a material containing dislocations to one Burgers vector only

A. I. Aptekarev — Spectral problems of highorder recurrences

Anne Boutet de Monvel, Igor Loutsenko and Oksana Yermolayeva — On the multifractal spectrum of the wholeplane LévyLoewner evolution

Anne Boutet de Monvel and Lech Zielinski — Asymptotic behavior of large eigenvalues of a modified JaynesCummings 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 onedimensional weighted Dirac operators

Alexandre Eremenko and Andrei Gabrielov — Spectral loci of SturmLiouville 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 nonselfadjoint ZakharovShabat 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 SturmLiouville problem from finite sets of spectral data

Ricardo Weder — Highvelocity estimates, inverse scattering and topological effects


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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

HansDieter Alber — The continuous theory of dislocations for a material containing dislocations to one Burgers vector only

A. I. Aptekarev — Spectral problems of highorder recurrences

Anne Boutet de Monvel, Igor Loutsenko and Oksana Yermolayeva — On the multifractal spectrum of the wholeplane LévyLoewner evolution

Anne Boutet de Monvel and Lech Zielinski — Asymptotic behavior of large eigenvalues of a modified JaynesCummings 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 onedimensional weighted Dirac operators

Alexandre Eremenko and Andrei Gabrielov — Spectral loci of SturmLiouville 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 nonselfadjoint ZakharovShabat 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 SturmLiouville problem from finite sets of spectral data

Ricardo Weder — Highvelocity estimates, inverse scattering and topological effects