Convergence for the regularized inversion of Fourier series |
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| Affiliation: | 1. Istituto per Applicazioni della Matematica CNR, Via Pietro Castellino, 111, 80131 Napoli, Italy;2. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Via Cintia, Monte S. Angelo, Napoli, Italy |
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| Abstract: | The problems of smoothing data through a transform in the Fourier domain and of retrieving a function from its Fourier coefficients are analyzed in the present paper. For both of them a solution, based on regularization tools, is known. Aim of the paper is to prove strong results of convergence of the regularized solution and optimality of the Generalized Cross Validation criterion for choosing the regularization parameter. |
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