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ambiguity function analytic extension analytic function applied arbitrary argument band-limited functions bounded linear Cauchy sequence chapter compact support complete orthonormal basis complex numbers computation consequence construction continuous function converges uniformly convolution decay defined denote derivatives discrete Equation estimate example formula Fourier coefficients Fourier series given harmonic function Hence identity implies inequality inner function interval inverse Fourier transform kernel L2-norm linear combination linear functional LP(T matrix Moreover multi-indices multiresolution approximation nonnegative nonzero norm observe open unit disc orthogonal orthonormal basis periodic function phase space Plancherel's theorem positive definite positive measure problem properties proposition Prove Remark result satisfies Schwartz class spectral measure square integrable stationary process straightforward subset subspace Suppose tempered distribution theory tion translation invariant trigonometric polynomial trigonometric series unit circle variable vector space verify wavelet yields Zak transform zero
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