**American Mathematical Society Translations - Series 2
Advances in the Mathematical Sciences**

2014; 251 pp; Hardcover

MSC: Primary 34; 35; 47; 60; 81;

Print ISBN: 978-1-4704-1683-6

Product Code: TRANS2/233

Print ISBN: 978-1-4704-1683-6

Product Code: TRANS2/233

List Price: $131.00

Individual Member Price: $104.80

**Electronic ISBN: 978-1-4704-1860-1
Product Code: TRANS2/233.E**

List Price: $131.00

Individual Member Price: $104.80

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# Spectral Theory and Differential Equations: V. A. Marchenko’s 90th Anniversary Collection

Share this page *Edited by *
*E. Khruslov; L. Pastur; D. Shepelsky*

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.

#### Table of Contents

# Table of Contents

## Spectral Theory and Differential Equations: V. A. Marchenko's 90th Anniversary Collection

- Cover Cover11
- Title page iii4
- Copyright page iv5
- Dedication v6
- Contents vii8
- Preface ix10
- Local inverse scattering problem as a tool of perturbation analysis for resonance systems 112
- The continuous theory of dislocations for a material containing dislocations to one Burgers vector only 2738
- Spectral problems of high-order recurrences 4354
- On the multi-fractal spectrum of the whole-plane Lévy-Loewner evolution 6374
- Asymptotic behavior of large eigenvalues of a modified Jaynes-Cummings model 7788
- Fourier integrals and a new representation of Maslov’s canonical operator near caustics 95106
- Inverse uniqueness results for one-dimensional weighted Dirac operators 117128
- Spectral loci of Sturm-Liouville operators with polynomial potentials 135146
- The central limit theorem for linear eigenvalue statistics of the sum of independent random matrices of rank one 145156
- On the spectrum of nonself-adjoint Zakharov-Shabat operators on ℝ 165176
- Homogenized model of oscillations of elastic medium with small caverns filled with viscous incompressible fluid 179190
- Double scaling limit in the Painlevé IV equation and asymptotics of the Okamoto polynomials 199210
- Recovering a potential of the Sturm-Liouville problem from finite sets of spectral data 211222
- High-velocity estimates, inverse scattering and topological effects 225236
- Back Cover Back Cover1266

#### Readership

Research mathematicians interested in spectral theory and differential operators and their applications.