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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
absolutely continuous analytic function Appell transformation apply Theorem arbitrary point assume belongs to H boundary boundary-value problem Cauchy's Chapter coefficients consequence of Theorem constant converges absolutely converges uniformly convolution Corollary cosh da(y defined Definition derivatives dominant series entire function example f k(x f_k(x finite interval follows 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 Huygens property hypothesis inequality integral representation integrand integration is valid inversion Laplace integral Laplace transform Lebesgue integrable Lemma notation obtain oo k(x Poisson integral Poisson transform Postulate power series rectangle region of convergence replaced result right-hand side satisfy the heat series expansion singularity source solution Stieltjes integral Stirling's formula t-axis t-plane temperature function term term-by-term integration Theorem 2.2 theorem is proved u e H uniqueness vanishes Widder x-axis zero
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Nonlinear Functional Analysis and Its Applications: Part 2 B: Nonlinear ...
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