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The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parameter sequences. Schur analysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricial generalizations. These problems include interpolation and moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices. This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrix-valued Carathéodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.
Differential equations -- Numerical solutions. --- Differential equations. --- Integral equations -- Numerical solutions. --- Interpolation --- Schur functions --- Inverse problems (Differential equations) --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Applied Mathematics --- Calculus --- Interpolation. --- Schur functions. --- Moment problems (Mathematics) --- S-functions --- Schur's functions --- Mathematics. --- Functions of complex variables. --- Integral transforms. --- Operational calculus. --- Operator theory. --- Operator Theory. --- Integral Transforms, Operational Calculus. --- Functions of a Complex Variable. --- Calculus, Operational --- Holomorphic functions --- Approximation theory --- Numerical analysis --- Integral Transforms. --- Complex variables --- Elliptic functions --- Functions of real variables --- Transform calculus --- Integral equations --- Transformations (Mathematics) --- Functional analysis --- Operational calculus --- Differential equations --- Electric circuits
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