5,255 research outputs found
On the Forelli-Rudin projection theorem
Motivated by the Forelli--Rudin projection theorem we give in this paper a
criterion for boundedness of an integral operator on weighted Lebesgue spaces
in the interval . We also calculate the precise norm of this integral
operator. This is the content of the first part of the paper. In the second
part, as applications, we give some results concerning the Bergman projection
and the Berezin transform. We derive a generalization of the Dostani\'{c}
result on the norm of the Berezin transform acting on Lebesgue spaces over the
unit ball in .Comment: to appear in Integral Equations and Operator Theor
Unified view of multimode algebras with Fock-like representations
A unified view of general multimode oscillator algebras with Fock-like
representations is presented.It extends a previous analysis of the single-mode
oscillator algebras.The expansion of the operators is
extended to include all normally ordered terms in creation and annihilation
operators and we analyze their action on Fock-like states.We restrict ourselves
to the algebras compatible with number operators. The connection between these
algebras and generalized statistics is analyzed.We demonstrate our approach by
considering the algebras obtainable from the generalized Jordan-Wigner
transformation, the para-Bose and para-Fermi algebras, the Govorkov
"paraquantization" algebra and generalized quon algebra.Comment: Latex, 34 pages, no figures ( accepted in Int.J.Theor.Phys.A
- β¦