In this work, we prove the existence and uniqueness of solution generalized Schrödinger equation in periodic distributional space P’. Furthermore, that depends continuously respect to initial data Introducing a family weakly continuous operators, is semigroup operators Then, with get fine version dependency theorem obtained. Finally, provide some consequences study.

In this paper an extensive study of the concepts generalized Green’s relations and GV -semigroups without order to ordered semigroups have been given. Our approach allows one see nature in class -ordered semigroups. Moreover we show that semigroup S is a if only complete semilattice completely π-regular Archimedean

This work considers the three-dimensional incompressible rotating magnetohydrodynamics equation spaces with fractional dissipation (−Δ)℘ for 12<℘≤1. Furthermore, we use Littlewood–Paley decomposition and frequency localization techniques to establish global well-posedness of equations in a more generalized Besov characterized by time evolution semigroup related linear Stokes–Coriolis operator.

A framework to describe a broad class of physical operations (including unitary transformations, dissipation, noise, and measurement) in a quantum optics experiment is given. This framework provides a powerful tool for assessing the capabilities and limitations of performing quantum information processing tasks using current experimental techniques. The Gottesman-Knill theorem is generalized to...

Skew convolution semigroups play an important role in the study of generalized Mehler semigroups and Ornstein-Uhlenbeck processes. We give a characterization for a general skew convolution semigroup on real separable Hilbert space whose characteristic functional is not necessarily differentiable at the initial time. A connection between this subject and catalytic branching superprocesses is est...

The Riesz basis property of the generalized eigenvector system of a Timoshenko beam with boundary feedback controls applied to two ends is studied in the present paper. The spectral property of the operator A determined by the closed loop system is investigated. It is shown that operator A has compact resolvent and generates a C0 semigroup, and its spectrum consists of two branches and has two ...

‎The present paper is devoted to the existence and uniqueness result of the fractional evolution equation $D^{q}_c u(t)=g(t,u(t))=Au(t)+f(t)$‎ ‎for the real $qin (0,1)$ with the initial value $u(0)=u_{0}intilde{R}$‎, ‎where $tilde{R}$ is the set of all generalized real numbers and $A$ is an operator defined from $mathcal G$ into itself‎. Here the Caputo fractional derivative $D^{q}_c$ is used i...