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Logarithmic Sobolev inequalities and the spectrum of Schrödinger operators. (English) Zbl 0471.58025


MSC:

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
58J65 Diffusion processes and stochastic analysis on manifolds
53C20 Global Riemannian geometry, including pinching
35Q99 Partial differential equations of mathematical physics and other areas of application
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[5] Girand, G., Problèmes mixtes et problèmes sur de variétés clos relativement aux équations linéaires du type elliptique, ANN. Soc. Pol. Math., 12, 35-54 (1933)
[6] Gross, L., Logarithmic Sobolev inequalities, Amer. J. Math., 97, 1061-1083 (1976) · Zbl 0318.46049
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[9] Rothaus, O., Lower bounds for eigenvalues of regular Sturm-Liouville operators and the logerithmic Sobolev inequality, Duke Math. J., 45, 351-362 (1978) · Zbl 0435.47049
[10] Rothaus, O., Logarithmic Sobolev inequalities and the spectrum of Sturm-Liouville operators, J. Funct. Anal., 39, 42-56 (1980) · Zbl 0472.47024
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