Result: Regions of meromorphy and value distribution of geometrically converging rational functions
Title:
Regions of meromorphy and value distribution of geometrically converging rational functions
Authors:
Source:
Journal of mathematical analysis and applications. 382(1):66-76
Publisher Information:
Amsterdam: Elsevier, 2011.
Publication Year:
2011
Physical Description:
print, 14 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Fonctions réelles, Real functions, Fonctions d'une variable complexe, Functions of a complex variable, Fonctions de plusieurs variables complexes et espaces analytiques, Several complex variables and analytic spaces, Approximations et développements, Approximations and expansions, Analyse mathématique, Mathematical analysis, Análisis matemático, Approximant Padé, Padé approximant, Aproximante Pade, Approximation Padé, Padé approximation, Aproximación Pade, Approximation Tchebychev, Chebyshev approximation, Aproximación Chebychev, Approximation fonction, Function approximation, Approximation rationnelle, Rational approximation, Aproximación racional, Convergence, Convergencia, Fonction méromorphe, Meromorphic function, Función meromorfa, Fonction rationnelle, Rational function, Función racional, Fonction répartition, Distribution function, Función distribución, 26Cxx, 30Dxx, 32A20, 41A21, Théorème Picard, Picard theorem, Distribution of zeros and poles, Harmonic majorant, Meromorphic functions, a-Values, m1-Maximal convergence
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Katholische Universität Eichstätt-Ingolstadt, Mathematisch-Geographische Fakultät, 85071 Eichstätt, Germany
Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, Acad. Bonchev Str. 8, 1113 Sofia, Bulgaria
Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, Acad. Bonchev Str. 8, 1113 Sofia, Bulgaria
ISSN:
0022-247X
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.24285114
Database:
PASCAL Archive
Further Information
Let D be a region, {rn}n∈ℕ a sequence of rational functions of degree at most n and let each rn have at most m poles in D, for m ∈ ℕ fixed. We prove that if {rn}n∈N converges geometrically to a function f on some continuum S ⊂ D and if the number of zeros of rn in any compact subset of D is of growth o(n) as n → ∞, then the sequence {rn}n∈ℕ converges m1-almost uniformly to a meromorphic function in D. This result about meromorphic continuation is used to obtain Picard-type theorems for the value distribution of m1-maximally convergent rational functions, especially in Padé approximation and Chebyshev rational approximation.