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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the estimation of the $ L\sb{2}$-norm of a function over a bounded subset of $ {\bf R}\sp{n}$


Author: Homer F. Walker
Journal: Proc. Amer. Math. Soc. 38 (1973), 103-110
MSC: Primary 46E35; Secondary 35J45
MathSciNet review: 0312250
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Abstract: The objective of this paper is to present an estimate bounding the $ {L_2}$-norm of a function over a bounded subset of $ {R^n}$ by the $ {L_2}$-norms of its derivatives of arbitrary order over all of $ {R^n}$ and the $ {L_2}$-norm of its projection onto a finite-dimensional space of functions with bounded support. The estimate essentially generalizes inequalities of Friedrichs [1, p. 284] and Lax and Phillips [2, p. 95]. An application of the estimate is made to the Fredholm theory of elliptic partial differential operators in $ {R^n}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0312250-7
PII: S 0002-9939(1973)0312250-7
Keywords: Calculus inequalities, Friedrichs inequality, first-order elliptic operators, indices of elliptic operators, Fredholm operators
Article copyright: © Copyright 1973 American Mathematical Society