Differential equations, mathematical physics, and applications : Selim Grigorievich Krein centennial / Peter Kuchment, Evgeny Semenov, editors.

Format:

Book

Author/Creator:

Kuchment, Peter

Contributor:

Kuchment, Peter, 1949- editor.

Semenov, E. M. (Evgeniĭ Mikhaĭlovich), editor.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 734

Contemporary mathematics, 734 0271-4132

Language:

English

Subjects (All):

Differential equations.

Mathematical physics.

Festschriften.

Kreĭn, S. G. (Selim Grigorʹevich), 1917-1999.

Kreĭn, S. G.

Physical Description:

1 online resource (322 pages).

Edition:

1st ed.

Other Title:

Selim Grigorievich Krein centennial

Place of Publication:

[Place of publication not identified] : American Mathematical Society, [2019]

Language Note:

English

Summary:

This is the second of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. The companion volume is Contemporary Mathematics, Volume 733.Krein was a major contributor to functional analysis, operator theory, partial differential equations, fluid dynamics, and other areas, and the author of several influential monographs in these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran, for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced mathematical life in the former Soviet Union.The articles contained in this volume are written by prominent mathematicians, former students and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter Schools. They are devoted to a variety of contemporary problems in ordinary and partial differential equations, fluid dynamics, and various applications.

Contents:

Cover

Title page

Contents

Preface

Introduction

1. Selim Grigorievich Krein and his mathematics

2. Some references

3. List of 83 S. Krein's PhD students

4. List of S. Krein's publications: books and papers

References

Voronezh Winter Mathematical School The presentation at the opening of the XXth School

1. Pre-history

2. The first school

3. The second school

4. The third school

5. The fourth school

6. A meeting at the Ministry of Higher Education of the Russian Federation

7. The sixth school

8. The seventh school

9. The impact of the school

Recollections of Mark Krein

Selim Krein and Voronezh Winter Mathematical Schools

A few words about our beloved teacher in mathematics and life

Probabilistic interpretations of quasilinear parabolic systems

1. SDEs and nonlinear parabolic equations

2. Probabilistic approach to nonlinear systems of parabolic equations

3. Probabilistic interpretation of the Cauchy problem viscosity solutions for parabolic systems with diagonal principal parts

4. Stochastic representation of the Cauchy problem solution for a system with cross-diffusion

Acknowledgement

On sectorial L-systems with Shrödinger operator

1. Introduction

2. Preliminaries

3. Realization of Stieltjes and inverse Stieltjes functions

4. Sectorial classes and their realizations

5. L-systems with Schrödinger operator

6. Sectorial L-systems with Schrödinger operator

The ^{ }-dissipativity of certain differential and integral operators

2. The scalar operators

3. ^{ }-dissipativity for systems

4. The ^{ }-dissipativity of the Lamé operator

5. The ^{ }-dissipativity of the "complex oblique derivative" operator.

6. ^{ }-positivity of certain integral operators

Probabilistic approach to a cell growth model

2. Mass process

3. Analytic properties of the limiting mass distribution density

4. Moments of total mass of population ( )

Acknowledgements

New examples of Hawking radiation from acoustic black holes

2. The number of particles operator

3. Hawking radiation from the simple rotating acoustic black hole

4. Hawking radiation from rotating acoustic black holes

5. The Hawking radiation in the case of black hole with corners

On multiplicative properties of determinants

2. Variational formulas

3. The structure of \res _{ }( ) and some special cases

4. Acknowledgment

Spectral properties of the Neumann-Laplace operator in quasiconformal regular domains

2. Composition operators and quasiconformal mappings

3. Poincaré-Sobolev inequalities

4. Eigenvalue Problem for Neumann-Laplacian

Acknowledgment

First steps of the global bifurcation theory in the plane

1. Class *( ²) vs generic families

2. Basic definitions.

3. Moduli of strong equivalence

4. Structurally unstable families

5. Global bifurcations in one-parameter families

6. Large bifurcation supports

7. Two-parameter families with separatrix polygons of codimension two

Spectral asymptotics for fractional Laplacians

1. Problem set-up

2. Preliminary analysis

3. Propagation of singularities near boundary

4. Reflection of singularities from the boundary

5. Main results

6. Appendices

7. Global theory

Comments

Spectral analysis and decomposition of normal operators related with the multi-interval finite Hilbert transform.

1. Introduction

2. Two simple cases

3. Resolvent operator in the case when \Iin consists of two or more subintervals

4. Solution of the RHP 3.1 and the jump of the resolvent kernel

5. Spectral properties of \CH*\CH and \CH\CH*.

Appendix A. Some auxiliary calculations

Polynomial-like elements in vector spaces with group actions

1. Polynomial-like elements

2. Polynomial-like elements in a ring

3. Polynomial-like elements related to lattices

Acknowledgments

On two hydromechanical problems inspired by works of S. Krein

The history of the problems

1. The case of ideal fluids in cavities of pendula.

2. The case of viscous fluids in cavities of pendula.

Adjoint discrete systems with properly stated leading terms

2. Problem statement

3. Index-0 systems

4. Index-1 systems

5. Index-2 systems

6. Conclusion

Solution of the initial value problem for the focusing Davey-Stewartson II system

2. The main result

3. Inverse problems for general scattering data

4. Derivation of the compatibility condition

5. Proof of Theorem 2.1

6. Acknowledgments

Vortex quantization in classical mechanics

1. Asymptotic solutions of the -particle Schrödinger equation as →∞ and superfluidity

2. Second quantization in the Fock's space. Schörnberg quantization. Macroscopic vorticity quantization.

Elliptic operators with nonstandard growth condition: Some results and open problems

2. Generalized -functions and functional spaces

3. Elliptic operators and Dirichlet problems

4. Convergence of solutions

5. Homogenization

References.

Essential spectrum of Schrödinger operators with and ′-interactions on systems of unbounded smooth hypersurfaces in ℝⁿ

2. Self-adjointness of the operators ℋ_{ _{Γ}, },ℋ_{ _{Γ}′, }

3. Delta-interactions on systems of parallel hyperplanes

4. Interaction on a system of slowly oscillating at infinity hypersurfaces

Back Cover.

Notes:

Description based on print version record.

Includes bibliographical references.

ISBN:

1-4704-5358-4