On Montessus de Ballore’s theorem for simultaneous Padé-Faber approximants

• Autorzy: Bosuwan N.

Identyfikatory

DOI

10.1515/dema-2018-0006

• Języki publikacji: EN

Abstrakty

EN

We consider row sequences of vector valued Padé-Faber approximants (simultaneous Padé-Faber approximants) and prove a Montessus de Ballore type theorem. Moreover, we provide a comparison between this new Montessus de Ballore type theorem and the Montessus de Ballore type theorem in Bosuwan (Math. Notes, 2018, 103).

Słowa kluczowe

EN

Montessus de Ballore’s theorem; Padé-Faber approximants; simultaneous Padé approximants; Hermite-Padé approximants

PL

twierdzenie Montessusa de Ballore'a; aproksymacja Padégo-Fabera; przybliżenia Padégo; aproksymacja Padégo; aproksymacja Hermite'a-Padégo

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2018
• Tom: Vol. 51, nr 1
• Strony: 45--61
• Opis fizyczny: Bibiogr. 14 poz.

Twórcy

autor

Bosuwan N.

• Department of Mathematics, Faculty of Science, Mahidol University, Rama VI Road, Ratchathewi District, Bangkok 10400, Thailand
• Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Bibliografia

• [1] Suetin P. K., Series of Faber Polynomials, Gordon and Breach Science Publishers, New York, 1998
• [2] Suetin S. P., On the convergence of rational approximations to polynomial expansions in domains of meromorphy of a given function, Math. USSR Sb., 1978, 34, 367-381
• [3] Suetin S. P., On Montessus de Ballore’s theorem for rational approximants of orthogonal expansions, Math. USSR Sb., 1982, 42, 399-411
• [4] Suetin S. P., On the existence of nonlinear Padé-Chebyshev approximations for analytic functions, Math. Notes, 2009, 86, 264-275
• [5] Cacoq J., de la Calle Ysern B., López Lagomasino G., Incomplete Padé approximation and convergence of row sequences of Hermite-Padé approximants, J. Approx. Theory, 2013, 170, 59-77
• [6] Graves-Morris P. R., Saff E. B., A de Montessus theorem for vector-valued rational interpolants, Lecture Notes in Math. 1105, Springer, Berlin, 1984, 227-242
• [7] Bosuwan N., Convergence of row sequences of simultaneous Padé-orthogonal approximants, Comput. Methods Funct. Theory, 2017, 17, 525-556
• [8] Bosuwan N., Convergence of row sequences of simultaneous Padé-Faber approximants, Math. Notes, 2018, accepted and expected to appear in vol. 103 arXiv:1709.04910v2
• [9] Smirnov V. I., Lebedev N. A., The constructive theory of functions of a complex variable, M.I.T. Press Cambridge, Mas-sachusetts, 1968
• [10] Curtiss. J. H., Faber polynomials and the Faber series, Amer. Math. Monthly, 1971, 78, 577-596
• [11] Gonchar A. A., On the convergence of generalized Padé approximants of meromorphic functions, Math. USSR Sb., 1975, 140, 564-577
• [12] Gonchar A. A., Poles of rows of the Padé table and meromorphic continuation of functions, Sb. Math., 1981, 43, 527-546
• [13] Sobczyk G., Generalized Vandermonde determinants and applications, Aportaciones Matematicas, Serie Comunicaciones, 2002, 30, 203-213
• [14] Gonchar A. A., Grigorjan L. D., On estimates of the norm of the holomorphic component of a meromorphic function, Sb. Math., 1976, 28, 571-575

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).