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Logarithmic Sobolev inequalities and the spectrum of Sturm-Liouville operators. (English) Zbl 0472.47024

MSC:
47E05 General theory of ordinary differential operators
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
26D10 Inequalities involving derivatives and differential and integral operators
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[1] Carmona, R, Regularity properties of Schrödinger and Dirichlet semigroups, J. functional analysis, 33, 259-296, (1979) · Zbl 0419.60075
[2] Gross, L, Logarithmic Sobolev inequalities, Amer. J. math., 97, 1061-1083, (1976) · Zbl 0318.46049
[3] Rothaus, O, Lower bounds for eigenvalues of regular Sturm-Liouville operators and the logarithmic Sobolev inequality, Duke math. J., 45, 351-362, (1978) · Zbl 0435.47049
[4] Weissler, F, Logarithmic Sobolev inequalities and hypercontractive estimates on the circle, J. functional analysis, 37, 218-234, (1980) · Zbl 0463.46024
[5] Adams, R; Clarke, F, Gross’s logarithmic Sobolev inequality, a simple proof, Amer. J. math., 101, 1265-1269, (1979) · Zbl 0421.46029
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