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EXPANSIONS IN A RECTANGLE
EXPANSIONS IN THE WHOLE PLANE
EXTENSIONS OF THE THEORY
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absolutely convergent Amer analytic function apply asymptotic Bessel functions Bessel inequality boundary condition bounded bounded variation Chapter Consider constant continuous function continuous partial derivatives converges in mean converges uniformly corresponding Courant and Hilbert defined denote differential equation dimensions discrete spectrum eigen eigenfunctions expansion formula finite interval finite number finite region fixed Fourier coefficients Fourier series function of L2 given Green's function integral equation involving iteration Laguerre polynomials last term left-hand side Lemma Let q(x Math multiplying neighbourhood obtain 00 one-dimensional orthogonal Parseval formula Parseval theorem perturbed eigenvalues perturbed equation poles positive number problem prove real axis rectangle regular replaced right-hand side Schwarz inequality second order second term similar argument similarly singularity solution spectra spectrum is discrete square summability Suppose tends to zero theory Titchmarsh uniformly convergent uniformly with respect unperturbed vanish whole plane