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Functions of complex variables --- Hilbert space --- Interpolation --- 517.518.8 --- Approximation theory --- Numerical analysis --- Banach spaces --- Hyperspace --- Inner product spaces --- Complex variables --- Elliptic functions --- Functions of real variables --- Approximation of functions by polynomials and their generalizations --- Functions of complex variables. --- Hilbert space. --- Interpolation. --- 517.518.8 Approximation of functions by polynomials and their generalizations

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Operator theory --- Complex analysis --- 51 <082.1> --- Mathematics--Series --- Schur functions --- Interpolation spaces. --- Moment problems (Mathematics) --- Lyapunov functions. --- Schur, Fonctions de --- Espaces d'interpolation --- Problèmes des moments (mathématiques) --- Interpolataion spaces --- Lyapunov functions --- S-functions --- Schur's functions --- Holomorphic functions --- Calculus, Operational --- Functions, Liapunov --- Liapunov functions --- Differential equations --- Schur, Fonctions de. --- Espaces d'interpolation.

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This book is dedicated to the memory of Israel Gohberg (1928–2009) – one of the great mathematicians of our time – who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg’s mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.

Operator theory. --- Operator theory --- Selfadjoint operators --- Free probability theory --- Operator algebras --- Functional analysis --- Differential equations, Partial --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Mathematics. --- Matrix theory. --- Algebra. --- Functional analysis. --- Functions of complex variables. --- System theory. --- Operator Theory. --- Functional Analysis. --- Several Complex Variables and Analytic Spaces. --- Linear and Multilinear Algebras, Matrix Theory. --- Systems Theory, Control. --- Differential equations, partial. --- Systems theory. --- Partial differential equations --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Systems, Theory of --- Systems science --- Science --- Mathematical analysis --- Complex variables --- Elliptic functions --- Functions of real variables --- Philosophy --- Gohberg, I. --- Gohberg, I. C., --- Gochberg, I. Z., --- Gokhberg, Izrailʹ T︠S︡udikovich. --- Gohberg, Israel, --- Gokhberg, Izrailʹ T︠S︡udikovich, --- Gokhberg, Yiśraʼel, --- Gokhberg, I. T︠S︡.

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Fourier series --- Fourier, Séries de --- 517.5 --- Fourier integrals --- Series, Fourier --- Series, Trigonometric --- Trigonometric series --- Calculus --- Fourier analysis --- Harmonic analysis --- Harmonic functions --- Theory of functions --- Fourier series. --- 517.5 Theory of functions --- Fourier, Séries de

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This largely self-contained treatment surveys, unites and extends some 20 years of research on direct and inverse problems for canonical systems of integral and differential equations and related systems. Five basic inverse problems are studied in which the main part of the given data is either a monodromy matrix; an input scattering matrix; an input impedance matrix; a matrix valued spectral function; or an asymptotic scattering matrix. The corresponding direct problems are also treated. The book incorporates introductions to the theory of matrix valued entire functions, reproducing kernel Hilbert spaces of vector valued entire functions (with special attention to two important spaces introduced by L. de Branges), the theory of J-inner matrix valued functions and their application to bitangential interpolation and extension problems, which can be used independently for courses and seminars in analysis or for self-study. A number of examples are presented to illustrate the theory.

Inverse problems (Differential equations) --- Integral equations --- Integral equations. --- Differential equations --- Equations, Integral --- Functional equations --- Functional analysis