An improvement to a Berezin-Li-Yau type inequality

Author:
Selma Yildirim Yolcu

Journal:
Proc. Amer. Math. Soc. **138** (2010), 4059-4066

MSC (2010):
Primary 35P15; Secondary 35S99

Published electronically:
May 18, 2010

MathSciNet review:
2679626

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Abstract: In this article we improve a lower bound for (a Berezin-Li-Yau type inequality) that appeared in an earlier paper of Harrell and Yolcu. Here denotes the th eigenvalue of the Klein Gordon Hamiltonian when restricted to a bounded set . can also be described as the generator of the Cauchy stochastic process with a killing condition on . To do this, we adapt the proof of Melas, who improved the estimate for the bound of , where denotes the th eigenvalue of the Dirichlet Laplacian on a bounded domain in .

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Additional Information

**Selma Yildirim Yolcu**

Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332

Address at time of publication:
Department of Mathematics, Georgia College & State University, Milledgeville, Georgia 31061; (after August 2010) Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Email:
selma@math.gatech.edu, selma.yildirim-yolcu@gcsu.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-2010-10419-7

Keywords:
Fractional Laplacian,
Weyl law,
universal bounds,
Klein-Gordon operator,
Berezin-Li-Yau inequality

Received by editor(s):
September 19, 2009

Received by editor(s) in revised form:
January 24, 2010

Published electronically:
May 18, 2010

Dedicated:
This paper is dedicated to Professor Evans M. Harrell

Communicated by:
Matthew J. Gursky

Article copyright:
© Copyright 2010
American Mathematical Society