TY - BOOK ID - 212831 TI - Interpolation, Schur Functions and Moment Problems AU - Alpay, Daniel AU - Gohberg, Israel. PY - 2006 SN - 1280613173 9786610613175 3764375477 3764375469 PB - Basel : Birkhäuser Basel : Imprint: Birkhäuser, DB - UniCat KW - Inverse problems (Differential equations) KW - Linear operators. KW - Toeplitz operators. KW - Hankel operators. KW - Wiener-Hopf operators. KW - Interpolation. KW - Schur functions. KW - Moment problems (Mathematics) KW - Calculus, Operational KW - S-functions KW - Schur's functions KW - Holomorphic functions KW - Approximation theory KW - Numerical analysis KW - Operators, Wiener-Hopf KW - Factorization of operators KW - Linear operators KW - Operators, Hankel KW - Integral operators KW - Operators, Toeplitz KW - Linear maps KW - Maps, Linear KW - Operators, Linear KW - Operator theory KW - Differential equations KW - Operator theory. KW - System theory. KW - Functional analysis. KW - Operator Theory. KW - Systems Theory, Control. KW - Functional Analysis. KW - Functional calculus KW - Calculus of variations KW - Functional equations KW - Integral equations KW - Functional analysis KW - Systems, Theory of KW - Systems science KW - Science KW - Philosophy KW - Systems theory. UR - https://www.unicat.be/uniCat?func=search&query=sysid:212831 AB - Schur analysis originates with an 1917 article of Schur where he associated to a function, which is analytic and contractive in the open unit disk, a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal processing, they are often named reflection coefficients. Under the word "Schur analysis" one encounters a variety of problems related to Schur functions, such as interpolation problems, moment problems, the study of the relationships between the Schur coefficients and the properties of the function, or the study of underlying operators. Such questions are also considered for some generalizations of Schur functions. Furthermore, there is an extension of the notion of a Schur function for functions that are analytic and have a positive real part in the open upper half-plane; these functions are called Carathéodory functions. This volume is almost entirely dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes. ER -