Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schroedinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schroedinger equation and some special and limiting cases are outlined.Comment: 17 pages, no figure

Rectangular differentiation of integrals of Besov functions

We study the differentiation of integrals of functions in the Besov spaces B α,1 p (R n), α> 0, 1 ≤ p < ∞, with respect to the basis of arbitrarily oriented rectangular parallelepipeds in R n. We show that positive results hold if α ≥ n−1 p and we give counterexamples for the case 0 < α <

On maximal functions over circular sectors with rotation invariant measures

summary:Given a rotation invariant measure in $\Bbb R^n$, we define the maximal operator over circular sectors. We prove that it is of strong type $(p,p)$ for $p>1$ and we give necessary and sufficient conditions on the measure for the weak type $(1,1)$ inequality. Actually we work in a more general setting containing the above and other situations

Formalisme, formalisation, intuition et compr\ue9hension en math\ue9matiques : de la pratique informelle aux syst\ue8mes formels et retour \ubb (\uab FFIUM \ubb)

"Ce projet cherche \ue0 comprendre l'interaction dynamique entre les th\ue9ories math\ue9matiques informelles et leur formalisation. Le terme ambigu\ueb \uab formalisation \ubb est au centre du projet." (dal progetto ufficiale