منابع مشابه
Multivariate Trace Inequalities
Abstract We prove several trace inequalities that extend the Golden-Thompson and the Araki-LiebThirring inequality to arbitrarily many matrices. In particular, we strengthen Lieb’s triple matrix inequality. As an example application of our four matrix extension of the Golden-Thompson inequality, we prove remainder terms for the monotonicity of the quantum relative entropy and strong sub-additiv...
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This paper describes sharp inequalities for the trace of Sobolev functions on the boundary of a bounded region Ω ⊂ R . The inequalities bound (semi-)norms of the boundary trace by certain norms of the function and its gradient on the region and two specific constants kρ and kΩ associated with the domain and a weight function. These inequalities are sharp in that there are functions for which eq...
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The existence of extremal functions for the Sobolev trace inequalities is studied using the concentration compactness theorem. The conjectured extremal, the function of conformal factor, is considered and is proved to be an actual extremal function with extra symmetry condition on functions. One of the limiting cases of the Sobolev trace inequalities is investigated and the best constant for th...
متن کاملOn Multivariate Grüss Inequalities
provided that f and g are two integrable functions on a, b such that p ≤ f x ≤ P , q ≤ g x ≤ Q, for all x ∈ a, b , where p, P, q, Q are real constants. Many generalizations, extensions, and variants of this inequality 1.1 have appeared in the literature, see 1–8 and the references given therein. The main purpose of the present paper is to establish several multivariate Grüss integral inequaliti...
متن کاملInequalities for Multivariate Polynomials
We summarize researches – in great deal jointly with my host Y. Sarantopoulos and his PhD students V. Anagnostopoulos and A. Pappas – started by a Marie Curie fellowship in 2001 and is still continuing. The project was to study multivariate polynomial inequalities. In the course of work we realized the role of the “generalized Minkowski functional”, to which we devoted a throughout survey. Resu...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2016
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-016-2778-5