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Chapter II BoundaryValue Problems
Chapter III Further Developments
Chapter IV Integral Transforms
Chapter V ThetaFunctions
Chapter VI Greens Function
Chapter VII Bounded Temperature Functions
Chapter VIII Positive Temperature Functions
Chapter IX The Huygens Property
analytic function Appell transformation apply Theorem assume belong to H boundary bounded Cauchy's Chapter constant continuous converges absolutely converges uniformly Corollary defined Definition derivatives dominant series dy ſ entire function example follows formula Fourier Fourier series Fubini's theorem function f(x function of H Green's function Green's theorem h-transform half-plane heat equation heat polynomials Hence homogeneous Huygens property hypothesis inequality integral representation integrand integration is valid inversion Laplace integral Laplace transform Lebesgue integrable Lemma obtain oo u(x Poisson integral Poisson transform Postulate rectangle region of convergence replaced result ſ k(x satisfy the heat series expansion ſh(x ſhe singularity ſk(x ſº source solution Stieltjes integral Stirling's formula strip t-plane temperature function term term-by-term integration Theorem 2.2 theorem is proved u e H vanishes variable Widder x-axis zero
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Nonlinear Functional Analysis and Its Applications: Part 2 B: Nonlinear ...
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