Geodesic
Existence and uniqueness of consistent Hermite – Fourier approximations
Problemy fiziki, matematiki i tehniki, no. 2 (2023), pp. 68-73

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The trigonometric analogues of algebraic Hermite – Padé approximations were defined, these are Hermite – Fourier approximations. In particular, the theorem of existence of Hermite – Fourier approximations was proved, the sufficient condition of their uniqueness was obtained, and the criterion of the existence and uniqueness of Hermite – Fourier polynomials, which are the numerator and denominator of Hermite – Fourier approximations associated with an arbitrary set of trigonometric series k. When the conditions of the criterion were met, the explicit type of the specified polynomials was established.
Keywords: trigonometric series, Fourier sums, trigonometric Padé approximants, Hermite – Padé polynomials, Hermite – Padé approximations. 
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     author = {A. P. Starovoitov and E. P. Kechko and T. M. Osnath},
     title = {Existence and uniqueness of consistent {Hermite} {\textendash} {Fourier} approximations},
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A. P. Starovoitov; E. P. Kechko; T. M. Osnath. Existence and uniqueness of consistent Hermite – Fourier approximations. Problemy fiziki, matematiki i tehniki, no. 2 (2023), pp. 68-73. http://geodesic.mathdoc.fr/item/PFMT_2023_2_a11/