Modern Analysis and Applications (eBook)

Contents 6
Preface 9
Mark Grigorievich Krein ( on his 100th birthday anniversary) 11
Part 1 Plenary Talks 23
Modified Krein Formula and Analytic Perturbation Procedure for Scattering on Arbitrary Junction 24
The Schur Transformation for Nevanlinna Functions: Operator Representations, Resolvent Matrices, and Orthogonal Polynomials 48
M. Krein’s Research on Semi-Bounded Operators, its Contemporary Developments, and Applications 85
Part 2 Research Papers 133
Remarks on the Inverse Spectral Theory for Singularly Perturbed Operators 134
An Approach to a Generalization of White Noise Analysis 142
Some Existence Conditions for the Compact Extrema of Variational Functionals of Several 159
Variables in Sobolev Space 159
The Moment Problem for Rational Measures: Convexity in the Spirit of Krein 174
Almost Periodic Factorization of Some Triangular Matrix Functions 187
On Generalized Operator-valued Toeplitz Kernels 207
Abstract Interpolation Problem in Nevanlinna Classes 212
On the Strong Kreiss Resolvent Condition in the Hilbert Space 252
Anatomy of the C*-algebra Generated by Toeplitz Operators with Piece- wise Continuous Symbols 258
Block Tridiagonal Matrices and a Beefed-up Version of the Ehrenfest Urn Model 281
On the Unitarization of Linear Representations of Primitive Partially Ordered Sets 292
Direct and Inverse Theorems in the Theory of Approximation of Banach Space Vectors by Exponential Type Entire Vectors 308
Results on Convergence in Norm of Exponential Product Formulas and Pointwise of the Corresponding Integral Kernels 328
Generalized Selfadjoint Operators 341
Orthogonal Decomposition of Functions Subharmonic in the Unit Disc 347
Asymptotics of Toeplitz Matrices with Symbols in Some Generalized Krein Algebras 353
Generators of Random Processes in Ultrametric Spaces and Their Spectra 372
On Pseudo-Hermitian Operators with Generalized C-symmetries 385
Nonisospectral Flows on Self-adjoint, Unitary and Normal Semi- infinite Block Jacobi Matrices 396
Compact Extrema: A General Theory and Its Applications to Variational Functionals 405
On Extremal Problem for Algebraic Polynomials in Loading Spaces 426
On Coxeter Graph Related Configurations of Subspaces of a Hilbert Space 436
Correlation Functions of Intrinsically Stationary Random Fields 458
Inverse Problem for Conservative Curved Systems 478