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Rational bases for spaces of holomorphic functions in the disc
Author(s) -
Kyriazis G.,
Petrushev P.
Publication year - 2014
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdt066
Subject(s) - holomorphic function , bounded function , mathematics , pure mathematics , basis (linear algebra) , rational function , identity theorem , unit (ring theory) , mathematical analysis , geometry , mathematics education
A new method for construction of bases for general distribution spaces is developed. This method allows the freedom to prescribe the nature and properties of the basis elements. The method is deployed to the construction of bases consisting of rational functions of uniformly bounded degrees for Besov and Triebel–Lizorkin spaces of holomorphic functions in the unit disc. In turn, this is utilized to give a new proof of Pekarski's direct estimate for rational approximation of holomorphic functions in H p .