Currently displaying 1 – 7 of 7

Showing per page

Order by Relevance | Title | Year of publication

Spectral properties of weakly almost periodic cosine functions

Valentina Casarino — 1998

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The spectral structure of the infinitesimal generator of a strongly continuous cosine function of linear bounded operators is investigated, under assumptions on the almost periodic behaviour of applications generated, in various ways, by C. Moreover, a first approach is presented to the analysis of connection between cosine functions and dynamical systems.

Equicontinuous families of operators generating mean periodic maps

Valentina Casarino — 1999

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The existence of mean periodic functions in the sense of L. Schwartz, generated, in various ways, by an equicontinuous group U or an equicontinuous cosine function C forces the spectral structure of the infinitesimal generator of U or C . In particular, it is proved under fairly general hypotheses that the spectrum has no accumulation point and that the continuous spectrum is empty.

Transferring L p eigenfunction bounds from S 2 n + 1 to hⁿ

Valentina CasarinoPaolo Ciatti — 2009

Studia Mathematica

By using the notion of contraction of Lie groups, we transfer L p - L ² estimates for joint spectral projectors from the unit complex sphere S 2 n + 1 in n + 1 to the reduced Heisenberg group hⁿ. In particular, we deduce some estimates recently obtained by H. Koch and F. Ricci on hⁿ. As a consequence, we prove, in the spirit of Sogge’s work, a discrete restriction theorem for the sub-Laplacian L on hⁿ.

L p - L q boundedness of analytic families of fractional integrals

Valentina CasarinoSilvia Secco — 2008

Studia Mathematica

We consider a double analytic family of fractional integrals S z γ , α along the curve t | t | α , introduced for α = 2 by L. Grafakos in 1993 and defined by ( S z γ , α f ) ( x , x ) : = 1 / Γ ( z + 1 / 2 ) | u - 1 | z ψ ( u - 1 ) f ( x - t , x - u | t | α ) d u | t | γ d t / t , where ψ is a bump function on ℝ supported near the origin, f c ( ² ) , z,γ ∈ ℂ, Re γ ≥ 0, α ∈ ℝ, α ≥ 2. We determine the set of all (1/p,1/q,Re z) such that S z γ , α maps L p ( ² ) to L q ( ² ) boundedly. Our proof is based on product-type kernel arguments. More precisely, we prove that the kernel K - 1 + i θ i ϱ , α is a product kernel on ℝ², adapted to the curve t | t | α ; as a consequence, we show that the operator...

Page 1

Download Results (CSV)