Some basic algebraic features of quasiparticle transformations are reviewed. Special nonlinear quasiparticle transformations are introduced leading to the second quantized counterparts of gerninal-type (correlated) wave functions. Algebraic representa-' tions of strong and weak orthogonality are discussed, and these issues are generalized to the case of non-orthogonal basis sets leading to the ...

We propose a very weak type of generalized distance called weak τ -function and use it to weaken the assumptions about lower semicontinuity in existing formulations of Ekeland’s variational principle for a kind of minimizers of a set-valued mapping, which is different from the Pareto minimizer, and in recent results which are equivalent to Ekeland’s variational principle.

We study the weak and strong type boundedness of maximal heat–diffusion operators associated with the system of generalized Hermite polynomials and with two different systems of generalized Hermite functions. We also give a necessary background to define Sobolev spaces in this context.

In this note we consider the maximal function for the generalized Ornstein-Uhlenbeck semigroup in R associated with the generalized Hermite polynomials {Hμ n} and prove that it is weak type (1,1) with respect to dλμ(x) = |x|2μe−|x| 2 dx, for μ > −1/2 as well as bounded on L(dλμ) for p > 1.

in this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted dirichlet spaces or bloch type spaces to $q_k$ type spaces.