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Integral equations --- Equations, Integral --- Functional equations --- Functional analysis

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Integral equations --- Numerical solutions --- Congresses --- -Equations, Integral --- Functional equations --- Functional analysis --- -Congresses --- -Numerical solutions --- Equations, Integral --- Numerical solutions&delete& --- Integral equations - Numerical solutions - Congresses

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517 --- Integral equations --- Equations, Integral --- Functional equations --- Functional analysis --- Analysis --- Integral equations. --- 517 Analysis

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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

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This volume includes several lecture notes on the fundamentals and elementary techniques of integrable field theories and on their applications to low-dimensional physics systems contributed by leading scientists in the respective fields. The main topics covered are various aspects of the thermodynamic Bethe ansatz, form factors, Calogero (and related) models, sigma models, conformal boundary conditions, etc. The volume presents both pedagogical material and a current research trend in the field.

Quantum field theory --- Integral equations --- Mathematical physics --- Equations, Integral --- Functional equations --- Functional analysis --- Numerical solutions