Polynomial approximation of regular functions of a quaternionic variable

• Autorzy: Szczepański Jerzy

Identyfikatory

DOI

10.55225/sti.441

• Języki publikacji: EN

Abstrakty

EN

We consider Bernstein-Walsh-Siciak-type theorems on the polynomial approximation in the case of regular functions of one quaternionic variable and their applications to the uniform approximation and approximation in Lp norms with respect to measures satisfying the Bernstein-Markov condition.

Słowa kluczowe

EN

quaternionic regular functions; polynomial approximation; Bernstein-Walsh-Siciak theorem; Bernstein-Markov condition; polynomial extremal function; Bernstein-Walsh inequality

PL

czwartorzędowe funkcje regularne; aproksymacja wielomianowa; twierdzenie Bernsteina-Walsha-Siciaka; warunek Bernsteina-Markowa; funkcja ekstremalna wielomianu; nierówność Bernsteina-Walsha

• Wydawca: Państwowa Wyższa Szkoła Zawodowa w Tarnowie
• Czasopismo: Science, Technology and Innovation
• Rocznik: 2022
• Tom: Vol. 16, no. 3-4
• Strony: 28--41
• Opis fizyczny: Bibliogr. 8 poz., fot.

Twórcy

autor

Szczepański Jerzy

• Jagiellonian University, Faculty of Mathematics and Computer Science, Poland

• https://orcid.org/0000-0002-1774-1425

Bibliografia

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• [2] Bloom T, Szczepański J. On the zeros of polynomials of best approximation. Journal of Approximation Theory. 1999;101(2):196–211. https://doi.org/10.1006/jath.1999.3381.
• [3] Gentili G, Struppa DC. A new theory of regular functions of a quaternionic variable. Advances in Mathematics. 2007;216(1):279–301. https://doi.org/10.1016/j.aim.2007.05.010.
• [4] Gentili G, Struppa DC. On the multiplicity of zeroes of polynomials with quaternionic coefficients, Milan Journal of Mathematics. 2008;76:15–25. https://doi.org/10.1007/s00032-008-0093-0 1997), 427–452
• [5] G.Gentili, C.Stoppato, D.C.Struppa, Regular Functions of a Quaternionic Variable, Springer Monographs in Mathematics, Springer-Verlag Berlin Heidelberg 2013
• [6] R.Jentzsch, Untersuchungen zur Theorie der Folgen analytischer Funktionen, Acta. Math., 41 (1918), 219–251
• [7] R. Serˆodio, Lok-Shun Siu, Zeros of Quaternion Polynomials, Applied Mathematics Letters, 14 (2001) 237–239
• [8] J.Siciak, On Some Extremal Functions and Their Applications in the Theory of Analytic Functions of Several Complex Variables, Trans. Amer. Math. Soc. 105(2), 1962, 322–357