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.
Author(s): Vadim Adamyan, Yu.M. Berezansky, Israel Gohberg, Myroslav L. Gorbachuk, Valentyna Gorbachuk, Anatoly N. Kochubei, Heinz Langer, Gennadi Popov
Series: Operator Theory: Advances and Applications
Edition: 1
Publisher: Birkhäuser Basel
Year: 2009
Language: English
Pages: 513
Contents......Page 6
Preface......Page 10
by V.M. Adamyan et al.......Page 12
by I. Gohberg......Page 22
Part 1: Plenary Talks......Page 24
Modified Krein Formula and Analytic Perturbation Procedure for Scattering on Arbitrary Junction......Page 26
The Schur Transformation for Nevanlinna Functions: Operator Representations, Resolvent Matrices, and Orthogonal Polynomials......Page 50
M. Kreĭn's Research on Semi-Bounded Operators, its Contemporary Developments, and Applicaions......Page 88
Part 2: Research Papers......Page 136
Remarks on the Inverse Spectral Theory for Singularly Perturbed Operators......Page 138
An Approach to a Generalization of White Noise Analysis......Page 146
Some Existence Conditions for the Compact Extrema of Variational Functionals of Several Variables in Sobolev Space W[sup(1)][sub(2)]......Page 164
The Moment Problem for Rational Measures: Convexity in the Spirit of Krein......Page 180
Almost Periodic Factorization of Some Triangular Matrix Functions......Page 194
On Generalized Operator-valued Toeplitz Kernels......Page 214
Abstract Interpolation Problem in Nevanlinna Classes......Page 220
On the Strong Kreiss Resolvent Condition in the Hilbert Space......Page 260
Anatomy of the C*-algebra Generated by Toeplitz Operators with Piece-wise Continuous Symbols......Page 266
Block Tridiagonal Matrices and a Beefed-up Version of the Ehrenfest Urn Model......Page 290
On the Unitarization of Linear Representations of Primitive Partially Ordered Sets......Page 302
Direct and Inverse Theorems in the Theory of Approximation of Banach Space Vectors by Exponential Type Entire Vectors......Page 318
Results on Convergence in Norm of Exponential Product Formulas and Pointwise of the Corresponding Integral Kernels......Page 338
Generalized Selfadjoint Operators......Page 352
Orthogonal Decomposition of Functions Subharmonic in the Unit Disc......Page 358
Asymptotics of Toeplitz Matrices with Symbols in Some Generalized Krein Algebras......Page 364
Generators of Random Processes in Ultrametric Spaces and Their Spectra......Page 384
On Pseudo-Hermitian Operators with Generalized C-symmetries......Page 398
Nonisospectral Flows on Self-adjoint, Unitary and Normal Semi-infinite Block Jacobi Matrices......Page 410
Compact Extrema: A General Theory and Its Applications to Variational Functionals......Page 420
On Extremal Problem for Algebraic Polynomials in Loading Spaces......Page 442
On Coxeter Graph Related Configurations of Subspaces of a Hilbert Space......Page 452
Correlation Functions of Intrinsically Stationary Random Fields......Page 474
Inverse Problem for Conservative Curved Systems......Page 494
