this article presents a unified approach to the abstract notions of partial convolution and involution in $l^p$-function spaces over semi-direct product of locally compact groups. let $h$ and $k$ be locally compact groups and $tau:hto aut(k)$ be a continuous homomorphism.  let $g_tau=hltimes_tau k$ be the semi-direct product of $h$ and $k$ with respect to $tau$. we define left and right $tau$-c...

The magnetic moment ($a_\gamma$) and weak ($a_W$) of charged leptons quarks are sensitive to quantum effects new physics heavy resonances. In effective field theory $a_\gamma$ $a_W$ induced by two independent operators, therefore, one has measure both the shed lights on physics. $a_W$'s SM fermions measured at LEP. this work, we analyze contributions from operators in processes $pp\to H \gamma$...

Given an open set $\Omega\subset\mathbb{R}^3$. We deal with the spectral study of Dirac operators form $H_{a,\tau}=H+A_{a,\tau}\delta_{\partial\Omega}$, where $H$ is free operator in $\mathbb{R}^3$, $A_{a,\tau}$ a bounded invertible, self-adjoint $\mathit{L}^{2}(\partial\Omega)^4$, depending on parameters $(a,\tau)\in\mathbb{R}\times\mathbb{R}^n$, $n\geqslant1$. investigate self-adjointness and...

Let $$L(t) = - \mathrm{div} \left( A(x,t) \nabla _x \right) $$ for $$t \in (0, \tau )$$ be a uniformly elliptic operator with boundary conditions on domain $$\Omega of $$\mathbb {R}^d$$ and $$\partial \frac{\partial }{\partial t}$$ . Define the parabolic $${{\mathcal {L}}}= \partial + L$$ $$L^2(0, , L^2(\Omega ))$$ by $$({{\mathcal {L}}}u)(t) := u(t)}{\partial t} L(t)u(t)$$ We assume very littl...

It is proved that bounded linear operators on Banach spaces of “cadlag” functions are measurable with respect to the Borel σ-algebra associated with the Skorokhod topology.

The fractional Laplacian $(-\Delta )^a$, $a\in(0,1)$, and its generalizations to variable-coefficient $2a$-order pseudodifferential operators $P$, are studied in $L_q$-Sobolev spaces of Bessel-potential type $H^s_q$. For a bounded open set $\Omega \subset \mathbb R^n$, consider the homogeneous Dirichlet problem: $Pu =f$ $, $u=0$ $ R^n\setminus\Omega $. We find regularity solutions determine exa...

relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $m$, called {em $tau$-rank of} $m$, which coincides with the reduced rank of $m$ whenever $tau$ is the goldie torsion theory. it is shown that the $tau$-rank of $m$ is measured by the length of certain decompositions of the $tau$-injective hull of $m$. moreover, some relations between the $tau$-rank of $m$ and c...

For every selfadjoint operator T in the Hilbert space H, f(T) makes sense not only in the obvious case where / is a polynomial but also if / is just measurable, and if fn(x)-+f(x) for all x£R (with (/,) bounded) then fn(T)-+f(T) weakly, i.e. <fn(T)£9i)+<f(T)£9ti)V£9fiCH. Moreover the set {f(T)9 f measurable} is the set of all operators S in H invariant under all unitary transformations of H whi...