Geodesic
On the existence of trigonometric Pad\'e approximations
Problemy fiziki, matematiki i tehniki, no. 3 (2024), pp. 71-76

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In this work, based on the well-known results on classical Padé approximants of power series, the conditions are found under which trigonometric Padé – Jacobi approximants exist for a given Fourier series. This made it possible to describe the class of Fourier series in Chebyshev polynomials of the first and second kind, for which there are nonlinear Padé – Chebyshev approximants. In particular, another proof of the well-known theorem of S.P. Suetin is given.
Mots-clés : Padé approximants
Keywords: Padé – Chebyshev approximations, power series, Fourier series, series in Chebyshev polynomials. 
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     title = {On the existence of trigonometric {Pad\'e} approximations},
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A. P. Starovoitov; T. M. Osnach; N. V. Ryabchenko. On the existence of trigonometric Pad\'e approximations. Problemy fiziki, matematiki i tehniki, no. 3 (2024), pp. 71-76. http://geodesic.mathdoc.fr/item/PFMT_2024_3_a11/