Modern Analysis and Applications

by Adamian, V. M.; Berezansky, Yurij; Gohberg, Israel; Gorbachuk, Myroslav; Gorbachuk, Valentyna

• ISBN13: 9783764399184
• ISBN10: 376439918X
• Format: Hardcover
• Copyright: 2009-06-01
• Publisher: Birkhauser

Summary

This is the first of two volumes containing peer-reviewed research and survey papers based on invited talks at the International Conference on Modern Analysis and Applications. The conference, which was dedicated to the 100th anniversary of the birth of Mark Krein, one of the greatest mathematicians of the 20th century, was held in Odessa, Ukraine, on April 9-14, 2007. The papers describe the contemporary development of subjects influenced by Krein, such as the theory of operators in Hilbert and Krein spaces, differential operators, applications of functional analysis in function theory, theory of networks and systems, mathematical physics and mechanics.

Table of Contents

Preface	p. ix
Mark Grigorievich Krein	p. xi
Plenary Talks
Modified Krein Formula and Analytic Perturbation Procedure for Scattering on Arbitrary Junction	p. 3
The Schur Transformation for Nevanlinna Functions: Operator Representations, Resolvent Matrices, and Orthogonal Polynomials	p. 27
M. Kre&ibrave;n's Research on Semi-Bounded Operators, its Contemporary Developments, and Applications	p. 65
Research Papers
Remarks on the Inverse Spectral Theory for Singularly Perturbed Operators	p. 115
An Approach to a Generalization of White Noise Analysis	p. 123
Some Existence Conditions for the Compact Extrema of Variational Functionals of Several Variables in Sobolev Space W12	p. 141
The Moment Problem for Rational Measures: Convexity in the Spirit of Krein	p. 157
Almost Periodic Factorization of Some Triangular Matrix Functions	p. 171
On Generalized Operator-valued Toeplitz Kernels	p. 191
Abstract Interpolation Problem in Nevanlinna Classes	p. 197
On the Strong Kreiss Resolvent Condition in the Hilbert Space	p. 237
Anatomy of the C*-algebra Generated by Toeplitz Operators with Piece-wise Continuous Symbols	p. 243
Block Tridiagonal Matrices and a Beefed-up Version of the Ehrenfest Urn Model	p. 267
On the Unitarization of Linear Representations of Primitive Partially Ordered Sets	p. 279
Direct and Inverse Theorems in the Theory of Approximation of Banach Space Vectors by Exponential Type Entire Vectors	p. 295
Results on Convergence in Norm of Exponential Product Formulas and Pointwise of the Corresponding Integral Kernels	p. 315
Generalized Selfadjoint Operators	p. 329
Orthogonal Decomposition of Functions Subharmonic in the Unit Disc	p. 335
Asymptotics of Toeplitz Matrices with Symbols in Some Generalized Krein Algebras	p. 341
Generators of Random Processes in Ultrametric Spaces and Their Spectra	p. 361
On Psuedo-Hermitian Operators with Generalized C-symmetries	p. 375
Nonisospectral Flows on Self-adjoint, Unitary and Normal Semi-infinite Block Jacobi Matrices	p. 387
Compact Extrema: A General Theory and Its Applications to Variational Functionals	p. 397
On Extremal Problem for Algebraic Polynomials in Loading Spaces	p. 419
On Coxeter Graph Related Configurations of Subspaces of a Hilbert Space	p. 429
Correlation Functions of Intrinsically Stationary Random Fields	p. 451
Inverse Problem for Conservative Curved Systems	p. 471
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