Abstract:
Extremal properties and localization of zeros of general (including nondiagonal) type I Hermite–Padé polynomials are studied for the exponential system {eλjz}kj=0 with arbitrary different complex numbers λ0,λ1,…,λk. The theorems proved in the paper complement and generalize the results obtained earlier by other authors.
Keywords:
exponential system, Hermite–Padé approximants, asymptotic equalities, zeros of a polynomial.
Citation:
A. P. Starovoitov, E. P. Kechko, “On Some Properties of Hermite–Padé Approximants to an Exponential System”, Complex analysis and its applications, Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar, Trudy Mat. Inst. Steklova, 298, MAIK Nauka/Interperiodica, Moscow, 2017, 338–355; Proc. Steklov Inst. Math., 298 (2017), 317–333
\Bibitem{StaKec17}
\by A.~P.~Starovoitov, E.~P.~Kechko
\paper On Some Properties of Hermite--Pad\'e Approximants to an Exponential System
\inbook Complex analysis and its applications
\bookinfo Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar
\serial Trudy Mat. Inst. Steklova
\yr 2017
\vol 298
\pages 338--355
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3835}
\crossref{https://doi.org/10.1134/S0371968517030190}
\elib{https://elibrary.ru/item.asp?id=30727078}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2017
\vol 298
\pages 317--333
\crossref{https://doi.org/10.1134/S0081543817060190}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000416139300019}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85036670638}
Linking options:
https://www.mathnet.ru/eng/tm3835
https://doi.org/10.1134/S0371968517030190
https://www.mathnet.ru/eng/tm/v298/p338
This publication is cited in the following 3 articles:
A. P. Starovoitov, E. P. Kechko, “Asymptotics for Hermite-pade approximants associated with the mittag-leffler functions”, Lobachevskii J. Math., 41:11, SI (2020), 2295–2302
M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov, “Skorost skhodimosti kvadratichnykh approksimatsii Ermita–Pade vyrozhdennykh gipergeometricheskikh funktsii”, PFMT, 2018, no. 1(34), 71–78
A. P. Starovoitov, “Hermite–Padé approximants of the Mittag-Leffler functions”, Proc. Steklov Inst. Math., 301 (2018), 228–244
Citation in format AMSBIB
Contact us: