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On approximation by exponentials. (English) Zbl 0893.41014

The approximation of functions from the \(L^2\) \([0,\infty]\) class on the positive semi-axis by linear combinations of exponentials \(\exp(- \lambda_\ell t)\) is investigated. The orthogonal basis for the approximation apparatus formation is built by means of the Fourier transform at \(\lambda_\ell =q^\ell\), \(\ell =0,1,2, \dots\), where \(q\in (0,1)\). A number of recurrence relations for orthogonal basis functions have been obtained. The convergence speed of approximation is investigated by using the inner product of the approximated function and finite linear combinations of the basis orthogonal functions.

MSC:

41A30 Approximation by other special function classes
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