Refined bounds for the eigenvalues of the Klein-Gordon operator
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Abstract:
The aim of this article is twofold. First we establish sharper lower bounds for the sums of eigenvalues of $(-\Delta )^{\frac {1}{2}}|_{D},$ 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 $(-\Delta )^{\frac {1}{2}}|_{D}.$References
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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
- Received by editor(s): February 6, 2012
- Published electronically: August 14, 2013
- Communicated by: Michael Hitrik
- © Copyright 2013 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 141 (2013), 4305-4315
- MSC (2010): Primary 35P15; Secondary 35P20
- DOI: https://doi.org/10.1090/S0002-9939-2013-11806-X
- MathSciNet review: 3105872