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Application of Mhaskar‐Prestin operators to the convergence of orthonormal expansions
Author(s) -
Mashele H. P.
Publication year - 2010
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310600
Subject(s) - mathematics , orthonormal basis , convergence (economics) , exponential function , polynomial , prestin , pure mathematics , mathematical analysis , combinatorics , anatomy , medicine , physics , quantum mechanics , cochlea , economics , outer hair cells , economic growth
Let I be either R or (–1, 1), and let W : I → (0, ∞). Assume that W 2 is a weight. We study the quasi‐interpolatory polynomial operators τ l , n , m introduced by Mhaskar and Prestin, for Freud weights, Erdös weights, and the exponential weights on (–1, 1). We investigate boundedness of τ l , n , m in weighted L p spaces. We then use this result to show thatfor even exponetial weights (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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