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A. Arnold, J. Bartier, J. Dolbeaut:
"Interpolation between logarithmic Sobolev and Poincaré inequalities";
in: "ASC Report 04/2007", herausgegeben von: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2007, ISBN: 978-3-902627-00-1.

This paper is concerned with intermediate inequalities which interpolate between
the logarithmic Sobolev (LSI) and the Poincar´e inequalities. Assuming that a given probability
measure gives rise to a LSI, we derive generalized Poincar´e inequalities, improving upon the known
constants from the literature. We also analyze the special case when these inequalities are restricted
to functions with zero components on the first eigenspaces of the corresponding evolution operator.

http://www.asc.tuwien.ac.at/preprint/2007/asc04x2007.pdf

Projektleitung Anton Arnold:
Numerik und Asymptotik mikroskopischer und makroskopischer Gleichungen für Quantensysteme