On sharp lower bounds for Calabi-type functionals and destabilizing properties of gradient flows

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

Weighted Energy-dissipation Functionals for Gradient Flows

We investigate a global-in-time variational approach to abstract evolution by means of the weighted energy-dissipation functionals proposed by Mielke & Ortiz [MO08]. In particular, we focus on gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow. Sharp convergence rates are ...

Sharp Bounds for the Tails of Functionals of Markov Chains

This paper is devoted to establishing sharp bounds for deviation probabilities of partial sums Σi=1f(Xi), where X = (Xn)n2N is a positive recurrent Markov chain and f is a real valued function defined on its state space. Combining the regenerative method to the Esscher transformation, these estimates are shown in particular to generalize probability inequalities proved in the i.i.d. case to the...

Lower Bounds of Copson Type for Hausdorff Matrices on Weighted Sequence Spaces

Let = be a non-negative matrix. Denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. If we used instead of The purpose of this paper is to establish a Hardy type formula for , where is Hausdorff matrix and A similar result is also established for where In particular, we apply o...

Lower bounds for generalized Ginzburg-Landau functionals