Examples are given of degenerate elliptic operators on smooth, compact manifolds that are not globally regular in C∞. These operators degenerate only in a rather mild fashion. Certain weak regularity results are proved, and an interpretation of global irregularity in terms of the associated heat semigroup is given.
Derndinger [Der80] and Krupa [Kru90] defined the F–product of a (strongly continuous one–parameter) semigroup (of linear operators) and presented some applications (e.g. to spectral theory of positive operators, cf. [EN00]). Wolff (in [Wol84] and [Wol00]) investigated some kind of nonstandard analogon and applied it to spectral theory of group representations. The question arises in which way t...
The norm convergence of the Trotter{Kato product formula is established with ultimate optimal error bound for the self-adjoint semigroup generated by the operator sum of two self-adjoint operators. A generalization is also given to the operator sum of several self-adjoint operators.
Journal:
:Discrete and Continuous Dynamical Systems-series B2023
<p style='text-indent:20px;'>We establish partial semigroup property of families Riemann-Liouville and Caputo fractional differential operators. Using this result we prove theorems on reduction multi-term systems to single-term multi-order systems. As an application obtain existence uniqueness solution systems.</p>
In this paper we consider stochastic differential equations on Banach spaces (not Hilbert). The system is semilinear and the principal operator generating a C0-semigroup is perturbed by a class of bounded linear operators considered as feedback operators from an admissible set. We consider the corresponding family of measure valued functions and present sufficient conditions for weak compactnes...
Let G be a semigroup of linear operators on a vector space S into itself with the operation of composition. A subset of G may be associated with a matroid X . We discuss the dimension of the kernels of certain linear operators induced in a natural way by the matroid structure on X .
A logarithm representation of evolution operators is defined. Generators of invertible evolution families are characterized by the logarithm representation. In this article, using the logarithm representation, a concept of evolution operators without satisfying the semigroup property is introduced. In conclusion the existence of alternative infinitesimal generator is clarified.
Let Tt be the semigroup of linear operators generated by a Schrödinger operator −A = ∆− V , where V is a nonnegative polynomial. We say that f is an element of H1 A if the maximal function Mf(x) = supt>0 |Ttf(x)| belongs to L1. A criterion on functions F which implies boundedness of the operators F (A) on H1 A is given.
The notion of automatic selfadjointness all ideals in a multiplicative semigroup the bounded linear operators on separable Hilbert space B(H) arose 2015 discussion with Heydar Radjavi who pointed out that and finite rank F(H) possessed this unitary invariant property which category we named SI semigroups (for selfadjoint ideal semigroups). Equivalent to is solvability, for each A semigroup, bil...
In this article we use the theory of C0-semigroup of bounded linear operators to establish the existence and uniqueness of a classical solution to a quasilinear functional differential equation considered in a Banach space.