5 papers
On the Fourier asymptotics of absolutely continuous measures with power-law singularities
M. Aloisio, S. L. de Carvalho, C. R. de Oliveira +1
We prove sharp estimates on the time-average behavior of the squared absolute value of the Fourier transform of some absolutely continuous measures that may have power-law singular…
A note on spectrum and quantum dynamics
Moacir Aloisio
We show, in the same vein of Simon's Wonderland Theorem, that, typically in Baire's sense, the rates with whom the solutions of the Schrödinger equation escape, in time average, fr…
Category theorems for Schrödinger semigroups
Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira
Stimulated by the category theorems of Eisner and Serény in the setting of unitary and isometric -semigroups on separable Hilbert spaces, we prove category theorems for Schröd…
Quantum quasiballistic dynamics and thick point spectrum
Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira
We obtain dynamical lower bounds for some self-adjoint operators with pure point spectrum in terms of the spacing properties of their eigenvalues. In particular, it is shown that f…
Refined scales of decaying rates of operator semigroups on Hilbert spaces: typical behaviour
Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira
We study relations between the decaying rates of operator semigroups on Hilbert spaces and some spectral properties of their respective generators; in particular, we show that the…