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1 summation of series 1
7 the Poisson summation formula 2 7 2 11 4
13 steadystate radiation in stars 3
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analytic application approximated band-limited functions bounded Cauchy's formula character Check circle complex numbers compute constant multiple converges defined Dirichlet kernel double coset eigenfunctions eigenvalue evaluation example EXERCISE 12 EXERCISE 9 exponential type expressed fact finish the proof finite fixed form a unit-perpendicular Fourier integral Fourier series Fourier transform function fe functions of class g e G group G half-plane Hardy function harmonic of weight Heisenberg's inequality Hilbert space Hint homomorphism indicator function inner product interval inversion formula isomorphic JG JG JQ JQ lattice Lebesgue Lebesgue integral lemma lim„Too means measurable modulus nonnegative perpendicular pick Plancherel identity plane Poisson summation formula pole polynomial prime problem proof is finished prove recipe Riemann Riemann-Lebesgue lemma rotation Section self-evident solution span spherical function spherical harmonics Step subgroup Subsection summable functions theorem unit-perpendicular basis unit-perpendicular family vanishes verify