Polynomial approximation of regular functions of a quaternionic variable
DOI:
https://doi.org/10.55225/sti.441Słowa kluczowe:
quaternionic regular functions, polynomial approximation, Bernstein-Walsh-Siciak theorem, Bernstein-Markov condition, polynomial extremal function, Bernstein-Walsh inequalityAbstrakt
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.
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Bloom TV. Orthogonal Polynomials in ℂn. Indiana University Mathematics Journal. 1997;46(2):427–452. Available from: https://www.jstor.org/stable/24899623. DOI: https://doi.org/10.1512/iumj.1997.46.1360 Google Scholar
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. DOI: https://doi.org/10.1006/jath.1999.3381 Google Scholar
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. DOI: https://doi.org/10.1016/j.aim.2007.05.010 Google Scholar
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. DOI: https://doi.org/10.1007/s00032-008-0093-0 Google Scholar
Gentili G, Stoppato C, Struppa DC. Regular Functions of a Quaternionic Variable. Cham: Springer; 2013. https://doi.org/10.1007/978-3-031-07531-5. DOI: https://doi.org/10.1007/978-3-642-33871-7 Google Scholar
Jentzsch R. Untersuchungen zur Theorie der Folgen analytischer Funktionen. Acta Mathematica. 1916;41:219–251. https://doi.org/10.1007/BF02422945. DOI: https://doi.org/10.1007/BF02422945 Google Scholar
Serôdio R, Lok-Shun Siu. Zeros of quaternion polynomials. Applied Mathematics Letters. 2001;14(2):237–239. https://doi.org/10.1016/S0893-9659(00)00142-7. DOI: https://doi.org/10.1016/S0893-9659(00)00142-7 Google Scholar
Siciak J. On some extremal functions and their applications in the theory of analytic functions of several complex variables. Transactions of the American Mathematical Society. 1962;105(2):322–357. https://doi.org/10.2307/1993631. DOI: https://doi.org/10.1090/S0002-9947-1962-0143946-5 Google Scholar
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Prawa autorskie (c) 2023 Jerzy Szczepański
Utwór dostępny jest na licencji Creative Commons Uznanie autorstwa – Na tych samych warunkach 4.0 Miedzynarodowe.
