Rothaus, O. S. Diffusion on compact Riemannian manifolds and logarithmic Sobolev inequalities. (English) Zbl 0471.58027 J. Funct. Anal. 42, 102-109 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 23 Documents MSC: 58J65 Diffusion processes and stochastic analysis on manifolds 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 60J60 Diffusion processes 53C20 Global Riemannian geometry, including pinching Keywords:estimates for the hypercontractive properties of the diffusion semigroup on compact oriented Riemannian manifolds; logarithmic Sobolev inequalities PDF BibTeX XML Cite \textit{O. S. Rothaus}, J. Funct. Anal. 42, 102--109 (1981; Zbl 0471.58027) Full Text: DOI References: [1] Faris, W., Product spaces and Nelson’s inequality, Helv. Phys. Acta, 48, 721-730 (1975) [2] Glimm, J., Boson fields with nonlinear interaction in two dimensions, Comm. Math. Phys., 8, 12-25 (1968) · Zbl 0173.29903 [3] Gross, L., Logarithmic Sobolev inequalities, Amer. J. Math., 97, 1061-1083 (1975) · Zbl 0318.46049 [4] Nelson, E., The free Markov field, J. Funct. Anal., 12, 211-227 (1973) · Zbl 0273.60079 [5] 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 [6] Rothaus, O., Logarithmic Sobolev inequalities and the spectrum of Sturm-Liouville operators, J. Funct. Anal., 39, 42-56 (1980) · Zbl 0472.47024 [8] Simon, B., A remark on Nelson’s best hypercontractive estimates, (Proc. Amer. Math. Soc., 55 (1976)), 376-378 · Zbl 0441.46026 [9] Weissler, F., Logarithmic Sobolev inequalities and hypercontractive estimates on the circle, J. Funct. Anal., 37, 218-234 (1980) · Zbl 0463.46024 [10] Hooton, J., Dirichlet forms associated with hypercontractive semigroups, Trans. Amer. Math. Soc., 253, 237-256 (1979) · Zbl 0424.47028 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.