Functional analysis and geometry : 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.

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

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 733

Contemporary mathematics, 733 0271-4132

Language:

English

Subjects (All):

Functional analysis.

Hyperbolic spaces.

Festschriften.

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

Kreĭn, S. G.

Physical Description:

1 online resource (314 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 first of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. The companion volume is Contemporary Mathematics, Volume 734.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 functional analysis, operator theory, several complex variables, topological dynamics, and algebraic, convex, and integral geometry.

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

My father Selim Krein

Kyiv, Fall of 1943 through 1946. The rebirth of mathematics

Selim Gregorievich Krein in Stony Brook

On algebraically integrable bodies

1. Introduction

2. Preliminaries

3. Proof of Theorem 1.5

Rearrangement invariant spaces satisfying Dunford-Pettis criterion of weak compactness

3. Some characterizations of the class of r.i. spaces satisfying Dunford-Pettis criterion of weak compactness

4. Orlicz spaces satisfying Dunford-Pettis criterion of weak compactness

5. The martingale difference Cesaro mean property in r.i. spaces

6. Reflexive subspaces of r.i. spaces satisfying Dunford-Pettis criterion of weak compactness

A new method of extension of local maps of Banach spaces. Applications and examples

2. Blid maps

3. Examples

4. Applications

5. More examples and open questions

Two consequences of the associativity condition for a hypercomplex system with locally compact basis

2. Definition of a hypercomplex system with a locally compact basis

3. The results

Inversion formulas of integral geometry in real hyperbolic space

3. Horospherical radon transforms

4. The totally geodesic Radon transforms

Acknowledgment

Total positivity, Grassmannian and modified Bessel functions

2. Positivity. Proof of Theorem 1.6

3. Acknowledgments

A remark on the intersection of plane curves.

Introduction

1. Focal loci

2. Double planes

3. The main result

4. Genera of subvarieties: a survey

Topological billiards, conservation laws and classification of trajectories

2. Outline of the general theory

3. Topological integrable billiards

4. Fomenko's conjecture. Modeling of any nondegenerate integrable system of general form with two degrees of freedom by an integrable topological billiard

5. The part of Fomenko's conjecture is correct. Kharcheva-Vedyushkina's theorem

6. The topology of the Liouville foliation of the billiards with nonconvex angles.

7. Integrable billiards in the Minkowski space

Hasse-Schmidt derivations and Cayley-Hamilton theorem for exterior algebras

2. Formulation of the results

3. Cayley-Hamilton Theorem revisited

4. Countably generated \QQ-vector spaces

5. Bosonic vertex operators

Acknowledgments

Complex analysis on the real sphere, or variations on a Maxwell's theme

1. Dual spherical polynomials (following Maxwell)

2. The Cauchy- Radon transform in ℝⁿ

3. The horospherical Cauchy transform on the sphere

4. The inversion of the horospherical Cauchy transform on the sphere

5. Relation to Maxwell polynomials

The weighted Laplace transform

2. Boundedness of _{ }

3. The operator ²_{ }

Surfaces with big automorphism groups

1. Danielewski's Surfaces

2. Gizatullin surfaces

3. Danilov-Gizatullin surfaces

4. \G_{ }-actions on normal surfaces

5. \A¹-fibrations

6. Amalgams

7. Generalized Gizatullin surfaces

Some binomial formulas for non-commuting operators

1. Formulation of main results.

2. Differential identities for some elementary functions

3. Proofs

4. Final remarks and conclusions

Similarity of holomorphic matrices on 1-dimensional Stein spaces

2. Notations and our use of the language of sheaves

3. Topological criteria for global holomorphic similarity

4. Bumps on Riemann surfaces

5. -adapted pairs of compact sets on 1-dimensional complex spaces

6. Jordan stable points

7. Proof of Theorem 1.2

Weighted geometric means of convex bodies

2. Weighted geometric means

3. A self-dual geometric mean

4. Additional remarks

Sobolev, Besov and Paley-Wiener vectors in Banach and Hilbert spaces

1. Introduction and main results

2. Lie groups and their representations

3. Hardy-Steklov operator associated with operators ₁, ₂,..., _{ }.

4. Interpolation spaces

5. Approximation by Hardy-Steklov averages, K-functor and modulus of continuity

6. Shannon sampling, Paley-Wiener frames and abstract Besov subspaces

7. Besov subspaces in Hilbert spaces

8. Applications

Toeplitz operators in polyanalytic Bergman type spaces

2. The structure of poly-Bergman and poly-Fock spaces

2.1. Polyanalytic and true polyanalytic spaces

2.2. The structure of the Fock spaces.

2.3. The structure of the Bergman spaces on the half-plane and on the disk.

3. Toeplitz operators with distributional symbols

3.1. Toeplitz operators in Bergman spaces on the disk and on the half-plane with symbols being derivatives of -C measures.

3.2. Toeplitz operators in \Fc with symbols being coderivatives of -FC measures.

4. Transformations of Toeplitz operators

4.1. Transformation of Toeplitz operators in the true poly-Bergman space on the half-plane.

4.2. Transformation of Toeplitz operators in the true poly-Bergman space on the disk.

4.3. Transformation of Toeplitz operators in the true poly-Fock space.

5. Properties of Toeplitz operators in true poly-Bergman type spaces

5.1. Compactness and degeneracy

5.1.1. Symbols with compact support and generalizations

5.1.2. Uniqueness

5.1.3. The finite rank property

5.2. Boundedness

Complete metric space of Riemann integrable functions and differential calculus in it

2. Space ₐₑ

3. Differentiation

4. Compositions

Acknowledgement

Back Cover.

Notes:

Description based on print version record.

Includes bibliographical references.

ISBN:

1-4704-5356-8