An estimate of the gap of the first two eigenvalues in the Schrödinger operator

I. M. Singer; Bun Wong; Shing-Tung Yau; Stephen S.-T. Yau

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1985)

  • Volume: 12, Issue: 2, page 319-333
  • ISSN: 0391-173X

How to cite

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Singer, I. M., et al. "An estimate of the gap of the first two eigenvalues in the Schrödinger operator." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 12.2 (1985): 319-333. <http://eudml.org/doc/83959>.

@article{Singer1985,
author = {Singer, I. M., Wong, Bun, Yau, Shing-Tung, Yau, Stephen S.-T.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {bounded convex domain; smooth boundary; nonnegative convex potential; first and second eigenvalue; Schrödinger operator; Dirichlet boundary condition; lower bound; upper bound; Malgrange preparation theorem},
language = {eng},
number = {2},
pages = {319-333},
publisher = {Scuola normale superiore},
title = {An estimate of the gap of the first two eigenvalues in the Schrödinger operator},
url = {http://eudml.org/doc/83959},
volume = {12},
year = {1985},
}

TY - JOUR
AU - Singer, I. M.
AU - Wong, Bun
AU - Yau, Shing-Tung
AU - Yau, Stephen S.-T.
TI - An estimate of the gap of the first two eigenvalues in the Schrödinger operator
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1985
PB - Scuola normale superiore
VL - 12
IS - 2
SP - 319
EP - 333
LA - eng
KW - bounded convex domain; smooth boundary; nonnegative convex potential; first and second eigenvalue; Schrödinger operator; Dirichlet boundary condition; lower bound; upper bound; Malgrange preparation theorem
UR - http://eudml.org/doc/83959
ER -

References

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  1. [1] Brascamp - Lieb, On extensions of the Brunn-Minkowski and prékopa-Leindler theorems, including inequalities for Log concave functions, and with an application to Diffusion equation, Journal of Functional Analysis, 22 (1976), pp. 366-389. Zbl0334.26009
  2. [2] S.Y. Cheng, Eigenvalue comparison theorems and its geometric applications, Math. Z., 143 (1975), pp. 289-297. Zbl0329.53035
  3. [3] Courant- Hilbert, Method of Mathematical Physics, Vol. I. Zbl0051.28802
  4. [4] P. Li - S.T. Yau, Estimate of eigenvalues of a compact Riemannian manifold, Proc. Symp. Pure Math., 36 (1980), pp. 205-240. Zbl0441.58014
  5. [5] B. Malgrange, Ideals of differentiable functions, Oxford University Press, 1966. Zbl0177.17902
  6. [6] Payne- Polya- Weinberger, On the ratio of consecutive eigenvalues, Journal of Math. and Physics, 35, No. 3 (Oct. 1956), pp. 289-298. Zbl0073.08203MR84696
  7. [7] B. Simon, The P(ϕ)2 Euclidean quantum field theory, Princeton Series in Physics. Zbl1175.81146

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