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Hankel operators are of wide application in mathematics (functional analysis, operator theory, approximation theory) and engineering (control theory, systems analysis) and this account of them is both elementary and rigorous. The book is based on graduate lectures given to an audience of mathematicians and control engineers, but to make it reasonably self-contained, the author has included several appendices on mathematical topics unlikely to be met by undergraduate engineers. The main prerequisites are basic complex analysis and some functional analysis, but the presentation is kept straightforward, avoiding unnecessary technicalities so that the fundamental results and their applications are evident. Some 45 exercises are included.

Hankel operators. --- Operator theory. --- Functional analysis --- Operators, Hankel --- Integral operators --- Hankel operators --- 517.983 --- 517.983 Linear operators. Linear operator equations --- Linear operators. Linear operator equations

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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.

Inverse problems (Differential equations) --- Linear operators. --- Toeplitz operators. --- Hankel operators. --- Wiener-Hopf operators. --- Interpolation. --- Schur functions. --- Moment problems (Mathematics) --- Calculus, Operational --- S-functions --- Schur's functions --- Holomorphic functions --- Approximation theory --- Numerical analysis --- Operators, Wiener-Hopf --- Factorization of operators --- Linear operators --- Operators, Hankel --- Integral operators --- Operators, Toeplitz --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Differential equations --- Operator theory. --- System theory. --- Functional analysis. --- Operator Theory. --- Systems Theory, Control. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Functional analysis --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Systems theory.