We prove asymptotic completeness for operators of the form H = −∆+L on L(R), d ≥ 2, where L is an admissible perturbation. Our class of admissible perturbations contains multiplication operators defined by real-valued potentials V ∈ L(R), q ∈ [d/2, (d + 1)/2] (if d = 2 then we require q ∈ (1, 3/2]), as well as real-valued potentials V satisfying a global Kato condition. The class of admissible ...

New algebraic structure on electronic Fock space is studied in detail. This structure is defined in terms of a certain multiplication of many electron wave functions and has close interrelation with coupled cluster and similar approaches. Its study clarifies and simplifies the mathematical backgrounds of these approaches. And even more, it leads to many relations that would be very difficult to...

Let V be an arbitrary system of weights on an open connected subset G of CN (N ≥ 1) and let B(E) be the Banach algebra of all bounded linear operators on a Banach space E. LetHVb (G,E) andHV0 (G,E) be the weighted locally convex spaces of vector-valued analytic functions. In this survey, we present a development of the theory of multiplication operators and composition operators from classical ...

In this paper, some classes of concerned multiplication operators consisting analytic and hyperbolic functions are defined considered. Furthermore, properties such as boundedness compactness the new discussed. Finally, a general class weighted Bloch is characterized by metric spaces.

We study Cwikel-type estimates for the singular values and Schatten Lp-norms of compositions multiplication convolution operators acting on stratified Lie groups. This enables us to obtain novel spectral asymptotic formulas certain derived from sub-Laplacians.

We recall the form factors f (j) N,N corresponding to the λ-extension C(N,N ;λ) of the two-point diagonal correlation function of the Ising model on the square lattice and their associated linear differential equations which exhibit both a “Russian-doll” nesting, and a decomposition of the linear differential operators as a direct sum of operators (equivalent to symmetric powers of the differen...

Let V be an arbitrary system of weights on an open connected subset G of CN (N ≥ 1) and let B(E) be the Banach algebra of all bounded linear operators on a Banach space E. LetHVb (G,E) andHV0 (G,E) be the weighted locally convex spaces of vector-valued analytic functions. In this survey, we present a development of the theory of multiplication operators and composition operators from classical ...

This paper is concerned with emptyness of the essential spectrum, or equivalently compactness of the semigroup, for perturbations of selfadjoint operators that are bounded below (on an L2-space). For perturbations by a (nonnegative) potential we obtain a simple criterion for compactness of the semigroup in terms of relative compactness of the operators of multiplication with characteristic func...

We propose an algebraic semantics for the temporal logic CTL∗ and simplify it for its sublogics CTL and LTL. We abstractly represent state and path formulas over transition systems in Boolean left quantales. These are complete lattices with a multiplication that preserves arbitrary joins in its left argument and is isotone in its right argument. Over these quantales, the semantics of CTL∗ formu...

This paper is concerned with the effective symbolic computation of operators under composition. Examples include differential operators under composition and vector fields under the Lie bracket. A basic fact about such operators is that, in general, they do not commute. A basic fact about applied mathematicians is that they often rewrite expressions involving noncommuting operators in terms of ...