Harnack inequality for two‐weight subelliptic p ‐Laplace operators

In this note, we prove a Harnack inequality for two‐weight subelliptic p ‐Laplace operators together with an upper bound of the Harnack constant associated with such inequality. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Weak convergence in Hilbert space and weak uncertainty relations in quantum theory

A suitable weak topology is considered on the Hilbert phase space of a quantum-mechanical system. It is then shown that if two bounded observables of the system have no common eigenvector, the sum of their variances in any state is always greater than some positive constant. Consequences of this result on some observables of simple physical systems are examined. First of all, the case of the position and momentum of the elementary particle in one dimension is studied and a comparation with Heisenberg's indeterminacy principle is carried out. Then, the case of angular variables is also examined, with special emphasis on spin 1/2. An experiment with neutrons is finally suggested and analysed with the help of the theory developed.     

On correlation function methods for detecting the stochastic transition

The use of correlation function methods to predict the onset of chaotic motion in conservative Hamiltonian systems is critically examined. It is shown that microcanonical correlation functions do not, in general, provide a convenient criterion to distinguish between stable and unstable motions.