A New Approach to the Analyticity of Some Classes of One-Parameter Semigroups in Weighted-LpSpaces (original) (raw)

Remarks on generators of analytic semigroups

Israel Journal of Mathematics, 1979

This paper contains two new characterizations of generators of analytic semigroups of linear operators in a Banach space. These characterizations do not require use of complex rn.mthers. One is used to give a new proof that strongly elliptic second order partial differential operators generate analytic semigroups in L~, 1 < p < ~~, while the sufficient condition in the other characterization is meaningful in the case of non-j linear operators.

ANALYTIC SEMIGROUPS AND THE ANGLE CONCAVITY THEOREM

We use the Stein's interpolation theorem in order to obtain an explicit positive lower bound for the angle of analyticity, whenever we interpolate between two analytic semigroups obtained as extensions of the same semigroup, but acting on dierent Lp spaces.

C -admissibility and analytic C -semigroups

Fuel and Energy Abstracts, 2011

We introduce the notion of C-admissible subspaces and obtain various conditions of C-admissibility, generalizing well known results of Vu and Schuler. Moreover, we show the uniqueness of solutions for the operator equation AX−XB=CD with A generating an analytic C-semigroup which generalize results of Vu.

On a class of positive C 0-semigroups of operators on weighted continuous function spaces

2011

This paper is mainly concerned with the study of the generators of those positive C0-semigroups on weighted continuous function spaces that leave invariant a given closed sub-lattice of bounded continuous functions and whose relevant restrictions are Feller semigroups. Additive and multiplicative perturbation results for this class of generators are also established. Finally, some applications concerning multiplicative perturbations of the Laplacian on R n , n ≥ 1, and degenerate second-order differential operators on unbounded real intervals are showed.

Estimates near the origin for functional calculus on analytic semigroups

2018

This paper provides sharp lower estimates near the origin for the functional calculus F(-uA) of a generator A of an operator semigroup defined on a sector; here F is given as the Fourier--Borel transform of an analytic functional. The results are linked to the existence of an identity element in the Banach algebra generated by the semigroup. Both the quasinilpotent and non-quasinilpotent cases are considered, and sharp results are proved extending many in the literature.

Interpolation of semigroups and integrated semigroups

Semigroup Forum, 1992

that any linear (unbounded) operator A on a Banach space E such that the resolvent set contains a half-line (w, cx~), generates a Co-semigroup on a certain (maximal) subspace Z of E (see also [Ka], [M-O-O], [Ne3]). This is a very general result, expressing the popular belief that linear dynamic systems are good-natured in some sense.

Degenerate Second Order Differential Operators Generating Analytic Semigroups inLp andW1,p

Mathematische Nachrichten, 2002

We deal with the problem of analyticity for the semigroup generated by the second order differential operator Au := αu + βu (or by some restrictions of it) in the spaces L p (0, 1), with or without weight, and in W 1,p (0, 1), 1 < p < ∞. Here α and β are assumed real-valued and continuous in [0, 1], with α(x) > 0 in (0, 1), and the domain of A is determined by the generalized Neumann boundary conditions and by Wentzell boundary conditions.

Semigroups of composition operators and integral operators in spaces of analytic functions

Annales Academiae Scientiarum Fennicae Mathematica, 2013

We study the maximal spaces of strong continuity on BM OA and the Bloch space B for semigroups of composition operators. Characterizations are given for the cases when these maximal spaces are V M OA or the little Bloch B 0 . These characterizations are in terms of the weak compactness of the resolvent function or in terms of a specially chosen symbol g of an integral operator T g . For the second characterization we prove and use an independent result, namely that the operators T g are weakly compact on the above mentioned spaces if and only if they are compact.