This work focuses on the well-posedness of abstract stochastic linear systems with boundary input delay and unbounded observation operators. We use product spaces a semigroup approach to reformulate such into free-delay distributed control gives us opportunity concept admissible operators as well Yosida extensions prove existence uniqueness solution process provide an estimation in relation ini...

We consider partial differential operators H = − div(C∇) in divergence form on R with a positive-semidefinite, symmetric, matrix C of real L∞-coefficients and establish that H is strongly elliptic if and only if the associated semigroup kernel satisfies local lower bounds, or, if and only if the kernel satisfies Gaussian upper and lower bounds.

For more details as regards semigroup theory of operators, see [1]. Fractional differential equations have been widely applied in many important areas, including thermodynamics, porous media, plasma dynamics, cosmic rays, continuum mechanics, electrodynamics, quantummechanics, biological systems and prime number theory [2, 3]. In particular, the fractional diffusion equations have been successf...

We show that every free semigroup algebras has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak-∗ closed unital operator operator algebra containing a weak-∗ dense subalgebra of compact operators has a unique Banach space predual.

In the framework of Hilbert spaces we shall give necessary and sufficient conditions to define a Dirichlet-to-Neumann operator via Dirichlet principle. Analyzing singular operators, will establish Laurent expansion near singularities as well Mittag–Leffler for related quadratic forms. The established results be exploited solve definitively problem positivity semigroup in Lebesgue spaces. obtain...

In this article, we deal with some problems involving a class of singularly perturbed elliptic operators. We prove the asymptotic preserving general Galerkin method associated to semilinear problem. use particular approximation estimate convergence rate on whole domain, for linear Finally, study behaviour semigroup generated.

Using a generalization of the semigroup theory of linear operators, we prove existence and uniqueness of S-asymptotically !-periodic mild solutions for a class of linear and semilinear fractional order differential equations of the form D +1 t u(t) + D t u(t)−Au(t) = f(t, u(t)), t > 0, 0 < ≤ ≤ 1, ≥ 0.

in [1,2,3], a. c. baker and j.w. baker studied the subspace ma(s) of the convolution measure algebra m, (s) of a locally compact semigroup. h. dzinotyiweyi in [5,7] considers an analogous measure space on a large class of c-distinguished topological semigroups containing all completely regular topological semigroups. in this paper, we extend the definitions to study the weighted semigroup algeb...