In this article the Jacquet module of a holomorphic representation is confuted by a direct and elementary method. The preliminary results involve the study of the notion of opposite parabolic subalgebra. * Research partially supported by an N . S . F . grant.

We deal with the problem of recovering a memory kernel k(t, η), depending on time t and on a spatial variable η, in a parabolic integro-differential equation related to a bounded domain Ω ⊂ R. We show that, under suitable assumptions and two pieces of additional information, our identification problem can be uniquely solved locally in time.

In this paper, we study the existence of global solutions for a class of impulsive abstract functional differential equation. An application involving a parabolic system with impulses is considered. c © 2008 Elsevier Ltd. All rights reserved.

In this paper we develop some of the foundations of the theory of relatively hyperbolic groups as originally formulated by Gromov. We prove the equivalence of two definitions of this notion. One is essentially that of a group admitting a properly discontinuous geometrically finite action on a proper hyperbolic space, that is, such that every limit point is either a conical limit point or a boun...

Acknowledgement: I thank to my supervisor Vladimír Souček for directing my study and research. Further, I thank to Svatopluk Kr´ysl for his permanent help.

In this paper, using a recent parabolic restriction estimate of Tao, we obtain improved partial results in the direction of Falconer’s distance set conjecture in dimensions d ≥ 3.

In this paper we calculate the parabolic class number of subgroups of Hecke groups H( √ 2),H( √ 3). Subject Classification: 20 G-H