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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

On $ \mathcal{C}^m$-approximability of functions by polynomial solutions of elliptic equations on plane compact sets


Author: K. Yu. Fedorovskiĭ
Translated by: the author
Original publication: Algebra i Analiz, tom 24 (2012), nomer 4.
Journal: St. Petersburg Math. J. 24 (2013), 677-689
MSC (2010): Primary 30E10, 41A30; Secondary 35J99
Published electronically: May 24, 2013
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Abstract: Conditions of $ \mathcal {C}^m$-approximability of functions by polynomial solutions of homogeneous elliptic equations of order $ n$ on plane compact sets are studied. For positive integers $ m$ and $ n$ such that $ m\geq n-1$, new necessary and sufficient approximability conditions of a topological and metrical nature are obtained.


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Additional Information

K. Yu. Fedorovskiĭ
Affiliation: Bauman Moscow State Technical University, Moscow 105005, Russia
Email: kfedorovs@yandex.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2013-01260-X
PII: S 1061-0022(2013)01260-X
Keywords: Homogeneous elliptic operator, $L$-analytic function, $L$-analytic polynomial, $\mathcal{C}^m$-approximation, localization operator
Received by editor(s): January 25, 2012
Published electronically: May 24, 2013
Additional Notes: The author was partially supported by RFBR (grant nos. 12-01-00434-a and 10-01-00837-a)
Article copyright: © Copyright 2013 American Mathematical Society