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Poincaré inequalities and hitting times

Patrick Cattiaux, Arnaud Guillin, Pierre André Zitt (2013)

Annales de l'I.H.P. Probabilités et statistiques

Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions is well known. We give here the correspondence (with quantitative results) for reversible diffusion processes. As a consequence, we generalize results of Bobkov in the one dimensional case on the value of the Poincaré constant for log-concave measures to superlinear potentials. Finally, we study various functional inequalities under different hitting times integrability conditions (polynomial,…)....

Remarks on strongly Wright-convex functions

Nelson Merentes, Kazimierz Nikodem, Sergio Rivas (2011)

Annales Polonici Mathematici

Some properties of strongly Wright-convex functions are presented. In particular it is shown that a function f:D → ℝ, where D is an open convex subset of an inner product space X, is strongly Wright-convex with modulus c if and only if it can be represented in the form f(x) = g(x)+a(x)+c||x||², x ∈ D, where g:D → ℝ is a convex function and a:X → ℝ is an additive function. A characterization of inner product spaces by strongly Wright-convex functions is also given.

Representation formula for the entropy and functional inequalities

Joseph Lehec (2013)

Annales de l'I.H.P. Probabilités et statistiques

We prove a stochastic formula for the Gaussian relative entropy in the spirit of Borell’s formula for the Laplace transform. As an application, we give simple proofs of a number of functional inequalities.

Solution of a Cauchy-Jensen stability Ulam type problem

John Michael Rassias (2001)

Archivum Mathematicum

In 1978 P. M. Gruber (Trans. Amer. Math. Soc. 245 (1978), 263–277) imposed the following general problem or Ulam type problem: “Suppose a mathematical object satisfies a certain property approximately. Is it then possible to approximate this objects by objects, satisfying the property exactly?" The afore-mentioned problem of P. M. Gruber is more general than the following problem imposed by S. M. Ulam in 1940 (Intersci, Publ., Inc., New York 1960): “Give conditions in order for a linear mapping...

Solution of a quadratic stability Ulam type problem

John Michael Rassias (2004)

Archivum Mathematicum

In 1940 S. M. Ulam (Intersci. Publ., Inc., New York 1960) imposed at the University of Wisconsin the problem: “Give conditions in order for a linear mapping near an approximately linear mapping to exist”. According to P. M. Gruber (Trans. Amer. Math. Soc. 245 (1978), 263–277) the afore-mentioned problem of S. M. Ulam belongs to the following general problem or Ulam type problem: “Suppose a mathematical object satisfies a certain property approximately. Is it then possible to approximate this objects...

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