Functional-analytic and Complex Methods, Their Interactions, and Applications to Partial Differential Equations: Proceedings of the International Graz Workshop, Graz, Austria, 12-16 February 2001
World Scientific, 2001 - Mathematics - 458 pages
Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today's rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations.This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell's equations, crystal optics, dynamical problems for cusped bars, and conservation laws.
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2 Applications of functionalanalytic and complex methods to mathematical physics
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Functional-analytic and Complex Methods, Their Interactions, and ...
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adjoint algebra analytic function applied arbitrary Bergman spaces boundary conditions boundary value problems bounded C(Dt Cauchy problem Clifford algebra Clifford analysis coefficients complex consider const constant cotangent defined Definition denote derivatives differential operators Dirac Dirac equation Dirac operator Dirichlet problem domain E-mail Eisenstein series finite number formula fundamental solution given holomorphic function homogeneous hyperbolic equations inequality infinity initial value problems integral equation isometry Lemma linear mapping Math Mathematics matrix method monogenic nonlinear obtain Ízk partial differential equations plane potential Proof proved quaternionic representation represented right-hand side satisfying the conditions second order singularities ſ║ solvable solved space strong generalized solution subspaces Suppose system of equations Theorem theory tions Tutschke unique vanishing variables vector zero