This is the ?rst 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 ofthebirthofMarkKrein,oneofthegreatestmathematiciansofthe20thcentury, was held in Odessa, Ukraine, on April 9-14, 2007. The conference focused on the main ideas, methods, results, and achievements of M. G. Krein. This?rstvolumeisdevotedtotheoperatortheoryandrelatedtopics. Itopens withthebiographypapersaboutM. G. Kreinandanumberofsurveypapersabout his work. The mainpartof the book consistsof originalresearchpaperspresenting the state of the art in operator theory and its application. The second volume of these proceedings, entitled Di?erential Operators and Mechanics, concerns other aspects of the conference. The two volumes will be of interest to a wide-range of readership in pure and applied mathematics, physics and engineering sciences. The editors are sincerely grateful to the persons who contributed to the preparation of these proceedings: Sergei Marchenko, Myroslav Sushko, Kostyantyn Yusenko and Vladimir Zavalnyuk. Mark Grigorievich Krein, 1907-1989 Operator Theory: Advances and Applications, Vol. 190, xi-xx c 2009 Birkh auser Verlag Basel/Switzerland Mark Grigorievich Krein (on his 100th birthday anniversary) V. M. Adamyan, D. Z. Arov, Yu. M. Berezansky, V. I. Gorbachuk, M. L. Gorbachuk, V. A. Mikhailets and A. M. Samoilenko April 3, 2007, is the l00th anniversary of the birth of Mark Grigorievich Krein, one of the most celebrated mathematicians of the 20th century, whose whole life was closely connected with Ukraine.

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