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Common terms and phrases1-periodic function a.e. x G assume B-spline Banach space bases Bessel sequence biorthogonal biorthogonal system bounded operator canonical dual frame Chapter ckfk coefficients compact support consider construct converges Corollary defined definition denote elements EmbTnag}m,n∈Z equivalent Example exists expansion fc=i fc=l fcez find finite sequences fk}kLi fk\kL following holds Fourier series Fourier transform frame decomposition frame operator frame sequence frame with frame function g Gabor frame Gabor system given Hilbert space implies inequality inner product invertible Lebesgue point Lemma lower frame bound matrix multiresolution analysis multiwavelet frames norm oblique dual obtain orthogonal projection orthonormal basis pre-frame operator proof Proposition prove pseudo-inverse representation result Riesz basis Riesz sequence satisfied Section self-adjoint sequence with bound shift-invariant systems shows Springer Science+Business Media Theorem tight frame trigonometric polynomial upper frame bound vector space wavelet frames wavelet set Bibliographic information
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