Notes on interpolation in the generalized Schur class. II. Nudel’man’s problem
Copyright policy )Notes on interpolation in the generalized Schur class. II. Nudel’man’s problem
An indefinite generalization of Nudel ′ ’ man’s problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides known results on existence criteria for Pick-Nevanlinna and Carathéodory-Fejér interpolation, the method yields new results on generalized interpolation in the sense of Sarason and boundary interpolation, including properties of the finite Hilbert transform relative to weights. The main theorem appeals to the Ball and Helton almost-commutant lifting theorem to provide criteria for the existence of a solution to Nudel ′ ’ man’s problem.
- The University of Texas at Dallas United States
- Ben-Gurion University of the Negev Israel
- University of Virginia United States
- University of Groningen Netherlands
- University of Virginia Main Campus United States
Nudelman's problem, Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces), M.G., interpolation problem, NEVANLINNA-PICK INTERPOLATION, Moment problems and interpolation problems in the complex plane, 47A57, 30E05, boundary interpolation, KREIN, Functional Analysis (math.FA), Mathematics - Functional Analysis, Linear operators on spaces with an indefinite metric, Algebra, Conjugate functions, conjugate series, singular integrals, FOS: Mathematics, Discrete Mathematics and Combinatorics, THEOREM, Hermitian form, Other Mathematics, Linear operator methods in interpolation, moment and extension problems
Nudelman's problem, Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces), M.G., interpolation problem, NEVANLINNA-PICK INTERPOLATION, Moment problems and interpolation problems in the complex plane, 47A57, 30E05, boundary interpolation, KREIN, Functional Analysis (math.FA), Mathematics - Functional Analysis, Linear operators on spaces with an indefinite metric, Algebra, Conjugate functions, conjugate series, singular integrals, FOS: Mathematics, Discrete Mathematics and Combinatorics, THEOREM, Hermitian form, Other Mathematics, Linear operator methods in interpolation, moment and extension problems
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