Download Interpolation, Schur Functions and Moment Problems by Daniel Alpay, Bernd Kirstein PDF

By Daniel Alpay, Bernd Kirstein

Schur research originates with a 1917 paper by way of Schur the place he linked to a functionality analytic and contractive within the open unit disk a series, finite or limitless, of numbers within the open unit disk, referred to as Schur coefficients. In sign processing, they can be referred to as mirrored image coefficients. below the note "Schur research" one encounters numerous difficulties concerning Schur capabilities akin to interpolation difficulties, second difficulties, examine of the relationships among the Schur coefficients and the houses of the functionality, examine of underlying operators and others.

This quantity is nearly fullyyt devoted to the research of Schur and Carathéodory features and to the recommendations of difficulties for those periods.

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Alpay, T. Ya. Azizov, A. Dijksma, H. Langer, and G. Wanjala, A basic interpolation problem for generalized Schur functions and coisometric realizations, Operator Theory: Adv. , vol. 143, Birkh¨ auser Verlag, Basel, 2003, 39–76. [4] D. Alpay, P. Bruinsma, A. V. de Snoo, Interpolation problems, extensions of symmetric operators and reproducing kernel spaces I, Operator Theory: Adv. 50, Birkh¨ auser Verlag, Basel, 1991, 35–82. [5] D. Alpay, P. Bruinsma, A. V. de Snoo, Interpolation problems, extensions of symmetric operators and reproducing kernel spaces II, Integral Equations Operator Theory 14 (1991) 465–500.

Langer, Uber einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im Raume Πκ zusammenh¨ angen, Teil II: Verallgemeinerte Resolventen, u-Resolventen und ganze Operatoren, J. Funct. Anal. 30(3) (1978), 390–447. G. Krein and H. Langer, On some extension problems which are closely connected with the theory of Hermitian operators in a space Πκ , III. Indefinite analogues of the Hamburger and Stieltjes moment problems. Part I, Beitr¨ age zur Anal. 14 (1979), 25–40. G. Krein and H.

16] L. de Branges, Espaces Hilbertiens de fonctions enti`eres, Masson, Paris, 1972. [17] M. Derevyagin, On the Schur algorithm for indefinite moment problem, Methods Funct. Anal. Topology 9(2) (2003), 133–145. [18] M. Derevyagin and V. Derkach, Spectral problems for generalized Jacobi matrices, Linear Algebra Appl. 382 (2004), 1–24. 28 D. Alpay, A. Dijksma, H. Langer and G. Wanjala [19] H. Dym, J-contractive matrix functions, reproducing kernel Hilbert spaces and interpolation, CBMS Regional Conference Series in Mathematics, 71.

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