Let (H,B) be an abstract Wiener space and let μs be the Gaussian measure on B with variance s. Let ∆ be the Laplacian (not the number operator), that is, a sum of squares of derivatives associated to an orthonormal basis of H. I will show that the heat operator exp(t∆/2) is a contraction operator from L2(B,μs) to L2(B,μs−t), for all t < s. More generally, the heat operator is a contraction from...

The work of von Neumann on Operator Theory as distinct from the later work on Rings of operators, extends from 1928 to 1932 with certain later additions. I t is a remarkable development in which the inadequacy of formula mathematics for quantum mechanics was established and a new abstract approach introduced. This approach required the abstract definition of Hubert space and reformulation of th...

Abstract. This paper presents necessary and sufficient conditions for a positive bounded operator on a separable Hilbert space to be the sum of a finite or infinite collection of projections (not necessarily mutually orthogonal), with the sum converging in the strong operator topology if the collection is infinite. A similar necessary condition is given when the operator and the projections are...

WAVE EQUATIONS AND ASSOCIATED DIRAC-TYPE OPERATORS FRITZ GESZTESY, JEROME A. GOLDSTEIN, HELGE HOLDEN, AND GERALD TESCHL Abstract. We discuss the unitary equivalence of generators GA,R associated with abstract damped wave equations of the type ü+Ru̇+A∗Au = 0 in some Hilbert spaceH1 and certain non-self-adjoint Dirac-type operatorsQA,R (away from the nullspace of the latter) in H1 ⊕ H2. The operat...

in this paper we study properties of symbols such that these belong to class of symbols sitting insidesm ρ,φ that we shall introduce as the following. so for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of m−hypoelliptic pseudodifferential operators for which define base on this class of symbols. also we consider maxi...

Database transformations provide a unifying framework for database queries and updates. Recently, it was shown that non-deterministic database transformations can be captured exactly by a variant of ASMs, the so-called Database Abstract State Machines (DB-ASMs). In this article we present a logic for DB-ASMs, extending the logic of Nanchen and Stärk for ASMs. In particular, we develop a rigorou...

Ordering optimisations are optimisations that can be applied to a concurrent logic program when the atoms of a clause are known to be ordered. In this paper ordering optimisations are reviewed, reformulated and refined. The paper explains how ordering optimisations can be realised in terms of abstract interpretation and shows that by, building on schedule analysis, simple, efficient and accurat...

General spectral boundary value problems framework is utilized to restate Poincaré, Hilbert, and Riemann problems for harmonic and analytic functions in the abstract operator-theoretic setting.

We propose a hierarchical abstract domain for the analysis of free-list memory allocators that tracks shape and numerical properties about both the heap and the free lists. Our domain is based on Separation Logic extended with predicates that capture the pointer arithmetics constraints for the heap-list and the shape of the free-list. These predicates are combined using a hierarchical compositi...

kinetic equations with positive collision operators Abstract We consider " forward-backward " parabolic equations in the abstract form Jdψ/dx+Lψ = 0, 0 < x < τ ≤ ∞, where J and L are operators in a Hilbert space H such that J = J * = J −1 , L = L * ≥ 0, and ker L = 0. The following theorem is proved: if the operator B = JL is similar to a self-adjoint operator, then associated half-range bounda...