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On stable methods of summing Fourier-Laplace series. (English) Zbl 0965.42019

Perturbation (in the \(\ell^2\) metric) of the Fourier coefficients may cause instability of the Fourier series in the space of continuous functions. A. N. Tikhonov found a stable approximation method for Fourier series. In the paper under review the same problem is solved for spherical harmonic series.

MSC:

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
34D10 Perturbations of ordinary differential equations
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
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References:

[1] A.N. Tikhonov, V.Y. Arsenin. Solutions of Ill-posed Problems. John Wiley & Sons, Inc., Winston, 1977 · Zbl 0354.65028
[2] A.N. Tikhonov. On Stable Method of Summing Fourier Series.Dokl. AN SSSR, 1964, 2: 268–271 (in Russian)
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