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Pseudoanalytic function theory generalizes and preserves many crucial features of complex analytic function theory. The Cauchy-Riemann system is replaced by a much more general first-order system with variable coefficients which turns out to be closely related to important equations of mathematical physics. This relation supplies powerful tools for studying and solving Schrödinger, Dirac, Maxwell, Klein-Gordon and other equations with the aid of complex-analytic methods. The book is dedicated to these recent developments in pseudoanalytic function theory and their applications as well as to multidimensional generalizations. It is directed to undergraduates, graduate students and researchers interested in complex-analytic methods, solution techniques for equations of mathematical physics, partial and ordinary differential equations.

Differential equations, Partial. --- Functions of complex variables. --- Pseudoanalytische Funktion. --- Sturm-Liouville-Differentialgleichung. --- Functions of complex variables --- Differential equations, Partial --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Complex variables --- Partial differential equations --- Mathematics. --- Operator theory. --- Partial differential equations. --- Physics. --- Partial Differential Equations. --- Mathematical Methods in Physics. --- Operator Theory. --- Functions of a Complex Variable. --- Several Complex Variables and Analytic Spaces. --- Elliptic functions --- Functions of real variables --- Differential equations, partial. --- Mathematical physics. --- Physical mathematics --- Physics --- Functional analysis --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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Pseudoanalytic function theory generalizes and preserves many crucial features of complex analytic function theory. The Cauchy-Riemann system is replaced by a much more general first-order system with variable coefficients which turns out to be closely related to important equations of mathematical physics. This relation supplies powerful tools for studying and solving Schrödinger, Dirac, Maxwell, Klein-Gordon and other equations with the aid of complex-analytic methods. The book is dedicated to these recent developments in pseudoanalytic function theory and their applications as well as to multidimensional generalizations. It is directed to undergraduates, graduate students and researchers interested in complex-analytic methods, solution techniques for equations of mathematical physics, partial and ordinary differential equations.

Analytical spaces --- Operator theory --- Functional analysis --- Partial differential equations --- Mathematical analysis --- Mathematical physics --- differentiaalvergelijkingen --- analyse (wiskunde) --- functies (wiskunde) --- wiskunde --- fysica

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Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones. Accordingly, they represent an important mathematical tool in the theory of inverse and scattering problems, of ordinary and partial differential equations, integral transforms and equations, special functions, harmonic analysis, potential theory, and generalized analytic functions. This volume explores recent advances in the construction and applications of transmutation operators, while also sharing some interesting historical notes on the subject. .

Differential equations. --- Partial differential equations. --- Integral transforms. --- Operational calculus. --- Functions of real variables. --- Potential theory (Mathematics). --- Ordinary Differential Equations. --- Partial Differential Equations. --- Integral Transforms, Operational Calculus. --- Real Functions. --- Potential Theory. --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Real variables --- Functions of complex variables --- Operational calculus --- Differential equations --- Electric circuits --- Integral equations --- Transform calculus --- Transformations (Mathematics) --- Partial differential equations --- 517.91 Differential equations --- Differential equations, Partial.

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This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.

Operator theory --- Mathematical analysis --- Mathematics --- analyse (wiskunde) --- wiskunde