Cesaro asymptotic equipartition of energy in the coupled case.
We study the mapping property of the commutator of Hardy-Littlewood maximal function on Triebel-Lizorkin spaces. Also, some new characterizations of the Lipschitz spaces are given.
Circular operators related to the operator of multiplication by a homomorphism of a locally compact abelian group and its restrictions are completely characterized. As particular cases descriptions of circular operators related to various quantum observables are given.
We investigate the criticality of the one term -order difference operators . We explicitly determine the recessive and the dominant system of solutions of the equation . Using their structure we prove a criticality criterion.