The convolution of associated homogeneous distributions on R – Part I

Convolution and Homogeneous Spaces

One - Dimensional Associated Homogeneous Distributions

Let H′ (R) denote the set of Associated Homogeneous Distributions (AHDs) with support in R. The set H′ (R) consists of the distributional analogues of one-dimensional power-log functions. H′ (R) is an important subset of the tempered distributions S′ (R), because (i) it contains the majority of the (one-dimensional) distributions typically encountered in physics applications and (ii) recent wor...

On the Associated Primes of the generalized $d$-Local Cohomology Modules

The first part of the paper is concerned to relationship between the sets of associated primes of the generalized $d$-local cohomology modules and the ordinary  generalized local cohomology  modules.  Assume that $R$ is a commutative Noetherian local ring, $M$ and $N$  are  finitely generated  $R$-modules and $d, t$ are two integers. We prove that $Ass H^t_d(M,N)=bigcup_{Iin Phi} Ass H^t_I(M,N)...

The Representations and Positive Type Functions of Some Homogenous Spaces

‎For a homogeneous spaces ‎$‎G/H‎$‎, we show that the convolution on $L^1(G/H)$ is the same as convolution on $L^1(K)$, where $G$ is semidirect product of a closed subgroup $H$ and a normal subgroup $K $ of ‎$‎G‎$‎. ‎Also we prove that there exists a one to one correspondence between nondegenerat $ast$-representations of $L^1(G/H)$ and representations of ...

A conceptual framework chemistry of Hydrated Cations: Part I. Preliminary Ab Initio and QTAIM calculations on [Li(H20)nr (n=1,2,3).

Ion molecules with general chemical formula as [Li(H2O)] (n=1,2,3), have been chosen as model species toinvestigate the chemical properties of hydrated lithium cations. The RHF(SCVS)/UGBS level of calculationhas been used for obtaining equilibrium geometries and Rho(r) functions (electron density distributions). By theaid of fundamental physical theorems implemented in Quantum Theory of Atoms i...