On the spectral gap for fixed membranes

Arkiv for Matematik

Volumn 39, Issue 1, 2001, Pages 65-74

  Davis, Burgess ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346278117     PISSN: 00042080     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02388791     Document Type: Article

References (17)

1. ASHBAUGH, M. S. and BENGURIA, R., Optimal lower bounds for eigenvalue gaps for Schrödinger operators with symmetric single-well potentials and related results, in Maximum Principles and Eigenvalue Problems in Partial Differential Equations (Knoxville, Tenn., 1987) (Schaefer, P. W., ed.), pp. 134-145, Longman, Harlow, 1988.
2. BAÑUELOS, R. and MENDEZ, P., Sharp inequalities for heat kernels of Schrödinger operators and applications to spectral gaps, J. Funct. Anal. 176 (2000), 368-399.
3. VAN DEN BERG, M., On condensation in the free-boson gas and the spectrum of the Laplacian, J. Statist. Phys. 31 (1983), 623-637.
4. BREIMAN, L., Probability, Addison-Wesley, Reading, Mass., 1969.
5. CHENG, S. Y., Eigenvalue comparison theorems and its geometric applications, Math. Z. 143 (1975), 289-297.
6. COURANT, R., FRIEDRICHS, K. and LEWY, H., On the partial difference equations of mathematical physics, Math. Ann. 100 (1928), 32-72.
7. DAVIES, E. B., Heat Kernels and Spectral Theory, Cambridge Univ. Press, Cambridge, 1989.
8. DAVIS, B. and MCDONALD, D., An elementary proof of the local central limit theorem, J. Theoret. Probab. 24 (1995), 693-701.
9. DYNKIN, E. B. and YUSKEVITCH, A., Markov Processes, Theorems and Problems, Plenum Press, New York, 1969.
10. KIRSCH, W. and SIMON, B., Comparison theorems for the gap of Schrödinger operators, J. Funct. Anal. 73 (1987), 396-410.
11. n, Michigan Math. J. 40 (1993), 259-270.
12. PAYNE, L., On two conjectures in the fixed membrane eigenvalue problem, J. Appl. Math. Phys. 24 (1973), 720-729.
13. POLLARD, D., Convergence of Stochastic Processes, Springer-Verlag, New York, 1984.
14. SALOFF-COSTE, L., Precise estimates on the rate at which certain diffusions tend to equilibrium, Math. Z. 217 (1994), 641-677.
15. SINGER, I. M., WONG, B., YAU, S. T. and YAU, S. S. T., An estimate of the gap of the first two eigenvalues in the Schrödinger operator, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 12 (1985), 319-333.
16. SMITS, R., Spectral gaps and rates to equilibrium in convex domains, Michigan Math. J. 43 (1996), 141-157.
17. YU, Q. and ZHONG, J. Q., Lower bounds of the gap between the first and second eigenvalues of the Schrödinger operator, Trans. Amer. Math. Soc. 294 (1986), 341-349.