Search results for "Semigroup"
showing 10 items of 96 documents
Isometric dilations and đ»^{â} calculus for bounded analytic semigroups and Ritt operators
2017
We show that any bounded analytic semigroup on L p L^p (with 1 > p > â 1>p>\infty ) whose negative generator admits a bounded H â ( ÎŁ Ξ ) H^{\infty }(\Sigma _\theta ) functional calculus for some Ξ â ( 0 , Ï 2 ) \theta \in (0,\frac {\pi }{2}) can be dilated into a bounded analytic semigroup ( R t ) t â©Ÿ 0 (R_t)_{t\geqslant 0} on a bigger L p L^p -space in such a way that R t R_t is a positive contraction for any t â©Ÿ 0 t\geqslant 0 . We also establish a discrete analogue for Ritt operators and consider the case when L p L^p -spaces are replaced by more general Banach spaces. In connection with these functional calculus issues, we study isometric dilations of bounded continuous repâŠ
From Resolvent Estimates to Semigroup Bounds
2019
In Chap. 10 we saw a concrete example of how to get resolvent bounds from semigroup bounds. Naturally, one can go in the opposite direction and in this chapter we discuss some abstract results of that type, including the HilleâYoshida and GearhardtâPrussâHwangâGreiner theorems. As for the latter, we also give a result of Helffer and the author that provides a more precise bound on the semigroup.
Cheeger-harmonic functions in metric measure spaces revisited
2014
Abstract Let ( X , d , Ό ) be a complete metric measure space, with Ό a locally doubling measure, that supports a local weak L 2 -Poincare inequality. By assuming a heat semigroup type curvature condition, we prove that Cheeger-harmonic functions are Lipschitz continuous on ( X , d , Ό ) . Gradient estimates for Cheeger-harmonic functions and solutions to a class of non-linear Poisson type equations are presented.
Feynman-Kac formulae
2015
In this chapter, we establish the connection between the deterministic EIT forward problem and the class of reflecting diffusion processes. We proceed along the lines of the recent paper [137] by Piiroinen and the author: We derive Feynman-Kac formulae in terms of these processes for the solutions to the forward problems corresponding to the continuum model and the complete electrode model, respectively. These results extend the classical Feynman-Kac formulae for elliptic boundary value problems in smooth domains and with smooth coefficients which were obtained in the 1980s and 1990s using the Feller semigroup approach and Ito stochastic calculus. In contrast to this well-studied situation,âŠ
Lévy flights and Lévy-Schrödinger semigroups
2010
We analyze two different confining mechanisms for L\'{e}vy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Levy-Schroedinger semigroups which induce so-called topological Levy processes (Levy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological L\'{e}vy process with the very same invariant pdf and in the reverse.
Common fixed point results on quasi-Banach spaces and integral equations
2013
In this paper we obtain fixed and common fixed point theorems for self-mappings defined on a closed and convex subset C of a quasi-Banach space. We give also a constructive method for finding the common fixed points of the involved mappings. As an application we obtain a result of the existence of solutions of integral equations.
On Associative Rings with Locally Nilpotent Adjoint Semigroup
2003
Abstract The set of all elements of an associative ring R, not necessarily with a unit element, forms a semigroup R ad under the circle operation r â s = r + s + rs for all r, s in R. This semigroup is locally nilpotent if every finitely generated subsemigroup of R ad is nilpotent (in sense of A. I. Mal'cev or B. H. Neumann and T. Taylor). The ring R is locally Lie-nilpotent if every finitely generated subring of R is Lie-nilpotent. It is proved that R ad is a locally nilpotent semigroup if and only if R is a locally Lie-nilpotent ring.
Jerarquies de models sigma: aplicacions a teories de Supergravetat i a teories conformes
2012
207 pĂĄginas. Tesis Doctoral del Departamento de FĂsica TeĂłrica, de la Universidad de Valencia. Fecha de lectura: 5 octubre 2012.
Sur une classe dâequations du type parabolique lineaires
1996
The application of the variational method for the existence theorem, developped by J. L. Lions, for the evolution equations in Hilbert spaces to a considerably large class of systems of linear partial differential equations of parabolic type is studied by defining Hilbert spaces in relation to the elliptic operator of the system, and an example insired by the system of equations for a viscous gas is examined.
Elliptic 1-Laplacian equations with dynamical boundary conditions
2018
Abstract This paper is concerned with an evolution problem having an elliptic equation involving the 1-Laplacian operator and a dynamical boundary condition. We apply nonlinear semigroup theory to obtain existence and uniqueness results as well as a comparison principle. Our main theorem shows that the solution we found is actually a strong solution. We also compare solutions with different data.