An improvement to a berezin-li-yau type inequality

Proceedings of the American Mathematical Society

Volumn 138, Issue 11, 2010, Pages 4059-4066

  Yolcu, Selma Yildirim ^a,b,c  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b GEORGIA COLLEGE AND STATE UNIVERSITY   (United States)

^c PURDUE UNIVERSITY   (United States)

Author keywords

Berezin Li Yau inequality; Fractional Laplacian; Klein Gordon operator; Universal bounds; Weyl law

Indexed keywords

EID: 78149275073     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-2010-10419-7     Document Type: Article

References (15)

1. N.I. Akhiezer and I.M. Glazman, Theory of Linear Operators in Hilbert Space, Vols. I, II, Pitman, 1981. MR0615736 (83i:47001a), MR0615737 (83i:47001b)
2. R. Bañuelos and T. Kulczycki, The Cauchy process and the Steklov problem, J. Funct. Analysis 211(2) (2004) 355-423. MR2056835 (2005b:60124)
3. R. Bañuelos and T. Kulczycki, Eigenvalue gaps for the Cauchy process and a Poincaré inequality, J. Funct. Analysis 234(1) (2006) 199-225. MR2214145 (2007c:60050)
4. R. Bañuelos, T. Kulczycki and Bartlomiej Siudeja, On the trace of symmetric stable processes on Lipschitz domains, J. Funct. Analysis 257(10) (2009) 3329-3352. MR2568694
5. F. A. Berezin, Covariant and contravariant symbols of operators, Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972) 1134-1167. MR0350504 (50:2996)
6. R. Blumenthal and R. Getoor, The asymptotic distribution of the eigenvalues for a class of Markov operators, Pacific J. Math. 9 (1959) 399-408. MR0107298 (21:6023)
7. E. M. Harrell II and L. Hermi, Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues, J. Funct. Analysis 254 (2008) 3173-3191. MR2418623 (2009f:47067)
8. E. M. Harrell II and S. Yildirim Yolcu, Eigenvalue inequalities for Klein-Gordon operators, J. Funct. Analysis, 256(12) (2009) 3977-3995. MR2521917
9. Alexei A. Ilyin, Lower bounds for the spectrum of the Laplace and Stokes operators, Discrete and Continuous Dynamical Systems, Volume 28, Number 1, September 2010, pp. 131-146. arXiv:0909.2818v1.
10. H. Kovařík, S. Vugalter and T. Weidl, Two dimensional Berezin-Li-Yau inequalities with a correction term, Comm. Math. Phys., 287(3) (2009), 959-981. MR2486669
11. A. Laptev and T. Weidl, Recent results on Lieb-Thirring inequalities, Journées "Équations aux Dérivées Partielles" (La Chapelle sur Erdre, 2000), Exp. No.XX, 14 pp., Univ. Nantes, Nantes, 2000. MR1775696 (2001j:81064)
12. P. Li and S.-T. Yau, On the Schrödinger equation and the eigenvalue problem, Comm. Math. Phys. 88 (1983) 309-318. MR701919 (84k:58225)
13. E. H. Lieb and M. Loss, Analysis, second edition. Graduate Studies in Mathematics 14, Providence, RI: Amer. Math. Soc. (2001). MR1817225 (2001i:00001)
14. A. D. Melas, A lower bound for sums of eigenvalues of the Laplacian, Proceedings of the American Mathematical Society 131(2) (2003) 631-636. MR1933356 (2003i:35218)
15. T. Weidl, Improved Berezin-Li-Yau inequalities with a remainder term, in Spectral Theory of Differential Operators, Amer. Math. Soc. Transl. Ser. 2, 225, Providence, RI: Amer. Math. Soc. (2008), 253-263. MR2509788