arXiv subjects

Angela A. Albanese

Publications and source records attributed to Angela A. Albanese.

23 records · Page 2Linked to original sources

arXiv2016

The Cesaro operator in growth Banach spaces of analytic functions

The Cesaro operator $\mathsf{C}$, when acting in the classical growth Banach spaces $A^{-γ}$ and $A_0^{-γ}$, for $γ> 0 $, of analytic functions on $\mathbb{D}$, is investigated. Based on a detailed knowledge of their spectra (due to A. Aleman and A.-M. Persson) we are able to determine the norms of these operators precisely. It is then possible to characterize the mean ergodic and related properties of $\mathsf{C}$ acting in these spaces. In addition, we determine the largest Banach space of analytic functions on $\mathbb{D}$ which $\mathsf{C}$ maps into $A^{-γ}$ (resp. into $A_0^{-γ}$); this optimal domain space always contains $A^{-γ}$ (resp. $A_0^{-γ}$) as a proper subspace.

math.FA↗

arXiv2013

Mean ergodic properties of the continuous Cesàro operators

Various properties of the (continuous) Cesàro operator $\mathsf{C}$, acting on Banach and Fréchet spaces of continuous functions and $L^p$-spaces, are investigated. For instance, the spectrum and point spectrum of $\mathsf{C}$ are completely determined and a study of certain dynamics of $\mathsf{C}$ is undertaken (eg. hyper- and supercyclicity, chaotic behaviour). In addition, the mean (and uniform mean) ergodic nature of $\mathsf{C}$ acting in the various spaces is identified.

math.FA↗

arXiv2013

One-dimensional degenerate diffusion operators

The aim of this paper is to present some results about generation, sectoriality and gradient estimates both for the semigroup and for the resolvent of suitable realizations of the operators [\Ab u(x)=γxu"(x) + b u'(x),] with constants $γ>0$ and $b\geq 0$, in the space $C([0,\infty])$

math.FA↗

arXiv2013

Analyticity for some degenerate evolution equations defined on domains with corners

We study the analyticity of the semigroups generated by some classes of degenerate second order differential operators in the space of continuous function on a domain with corners. These semigroups arise from the theory of dynamics of populations.

math.FA↗

arXiv2010

Analyticity of a class of degenerate evolution equations on the canonical simplex of $\R^d$ arising from Fleming--Viot processes

We study the analyticity of the semigroups generated by a class of degenerate second order differential operators in the space $C(S_d)$, where $S_d$ is the canonical simplex of $\R^d$. The semigroups arise from the theory of Fleming--Viot processes in population genetics.

math.FA↗