Ebook: Operator Theory, System Theory and Related Topics: The Moshe Livšic Anniversary Volume

This volume presents the refereed proceedings of the Conference in Operator The­ ory in Honour of Moshe Livsic 80th Birthday, held June 29 to July 4, 1997, at the Ben-Gurion University of the Negev (Beer-Sheva, Israel) and at the Weizmann In­ stitute of Science (Rehovot, Israel). The volume contains papers in operator theory and its applications (understood in a very wide sense), many of them reflecting, 1 directly or indirectly, a profound impact of the work of Moshe Livsic. Moshe (Mikhail Samuilovich) Livsic was born on July 4, 1917, in the small town of Pokotilova near Uman, in the province of Kiev in the Ukraine; his family moved to Odessa when he was four years old. In 1933 he enrolled in the Department of Physics and Mathematics at the Odessa State University, where he became a student of M. G. Krein and an active participant in Krein's seminar - one of the centres where the ideas and methods of functional analysis and operator theory were being developed. Besides M. G. Krein, M. S. Livsic was strongly influenced B. Va. Levin, an outstanding specialist in the theory of analytic functions. A by deep understanding of operator theory as well as function theory and a penetrating search of connections between the two, were to become one of the landmarks of M. S. Livsic's work. M. S. Livsic defended his Ph. D.

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The present selection of refereed papers is dedicated to Moshe Liv_ic on the occasion of his eightieth anniversary. It covers many areas of operator theory and its applications, reflecting the breadth and the profound impact of his work. In particular, some of his most recent ideas on 2D-systems are presented. Other contributions cover important avenues of modern operator theory in such fields as interpolation theory (also in the so-called nonstationary setting), direct and inverse problems for the string equation and for nonselfadjoint differential operators, operator models and function theory. The volume will appeal to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.

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The present selection of refereed papers is dedicated to Moshe Liv_ic on the occasion of his eightieth anniversary. It covers many areas of operator theory and its applications, reflecting the breadth and the profound impact of his work. In particular, some of his most recent ideas on 2D-systems are presented. Other contributions cover important avenues of modern operator theory in such fields as interpolation theory (also in the so-called nonstationary setting), direct and inverse problems for the string equation and for nonselfadjoint differential operators, operator models and function theory. The volume will appeal to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
Content:
Front Matter....Pages i-xi
List of Publications of M. S. Liv?ic....Pages 1-5
Vortices of 2D Systems....Pages 7-41
Realization and Factorization in Reproducing Kernel Pontryagin Spaces....Pages 43-65
Models of Contractions Constructed from the Defect Function of Their Characteristic Function....Pages 67-87
Measure Schur Complements and Spectral Functions of Unitary Operators with Respect to Different Scales....Pages 89-138
On the Second Order Interpolation for Rational Vector Functions....Pages 139-159
Generalized Moments, Center-Focus Conditions, and Compositions of Polynomials....Pages 161-185
Inverse Spectral problem for the Sturm-Liouville Operator with Eigenvalue Parameter Dependent Boundary Conditions....Pages 187-194
A Module Approach to Commutant Lifting on Kre?n Spaces....Pages 195-206
On Dual Canonical Systems and Dual Matrix String Equations....Pages 207-228
Bitangential Interpolation for Upper Triangular Operators with Infinitely Many Interpolation Nodes....Pages 229-256
Some Applications of Operator-valued Herglotz Functions....Pages 257-270
Analogues of a Theorem of Frostman on Linear Fractional Transformations of Inner Functions and the Typical Spectral Structure of Analytic Families of Weak Contractions....Pages 271-321
Right and Left Joint System Representation of a Rational Matrix Function in General Position....Pages 323-336
One-parameter Semigroups of Fractional-linear Transformations....Pages 337-400
Scattering from an Impurity: Lax-Phillips Approach....Pages 401-411
Spectral Theory of Wiener-Hopf Operators and Functional Model....Pages 413-431
Operator Dilations with Prescribed Commutators....Pages 433-452
Condition of Orthogonality of Spectral Matrix Function....Pages 453-460
Functional Models of Linear Operators....Pages 461-468
Non-self-adjoint Periodic Dirac Operators....Pages 469-484
A Note on Hyponormal Operators Associated with Quadrature Domains....Pages 485-512
Two Remarks on Fuchsian Groups of Widom Type....Pages 513-525
A Functional Model for the Lie Algebra SL(2, ?) of Linear Non-self-adjoint Operators....Pages 527-537
....Pages 539-567