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

 

Refined bounds for the eigenvalues of the Klein-Gordon operator


Author: Türkay Yolcu
Journal: Proc. Amer. Math. Soc. 141 (2013), 4305-4315
MSC (2010): Primary 35P15; Secondary 35P20
Published electronically: August 14, 2013
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Abstract: The aim of this article is twofold. First we establish sharper lower bounds for the sums of eigenvalues of $ (-\Delta )^{\frac {1}{2}}\vert _{D},$ the Klein-Gordon operator restricted to a bounded domain $ D\subset {\mathbb{R}}^d,$ than the bounds obtained in works by E. Harrell; S. Yıldırım Yolcu; and G. Wei, H. Sun, and L. Zeng. Then we study upper bounds for the sums of negative powers of the eigenvalues of $ (-\Delta )^{\frac {1}{2}}\vert _{D}.$


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Additional Information

Türkay Yolcu
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Address at time of publication: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106
Email: tyolcu@math.purdue.edu, tyolcu@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11806-X
PII: S 0002-9939(2013)11806-X
Keywords: Berezin-Li-Yau, counting function, eigenvalue, inequality, Klein-Gordon
Received by editor(s): February 6, 2012
Published electronically: August 14, 2013
Communicated by: Michael Hitrik
Article copyright: © Copyright 2013 American Mathematical Society