harmonic analysis, homological algebra, and operator spaces

In the analysis of logic programs, abstract domains for detecting sharing properties are widely used. Recently the new domain ShLin has been introduced to generalize both sharing and linearity information. This domain is endowed with an optimal abstract operator for single-binding unification. The authors claim that the repeated application of this operator is also optimal for multi-binding uni...

Finiteness of the point spectrum of linear operators acting in a Banach space is investigated from point of view of perturbation theory. In the first part of the paper we present an abstract result based on analytical continuation of the resolvent function through continuous spectrum. In the second part, the abstract result is applied to differential operators which can be represented as a diff...

Zonotopes are a convenient abstract domain for the precise analysis of programs with numerical variables. Compared to the domain of convex polyhedra, it is less expensive and may easily handle non-linear assignments. However, the classical join operator of this abstract domain does not always preserve linear invariants, unlike the convex hull. We present a global join operator that preserves so...

We give a survey of how the relatively young theory of operator spaces has led to a deeper understanding of the Fourier algebra of a locally compact group (and of related algebras).

Generalized Quasilinearization Method for Coincidences Adriana Buică and Radu Precup Faculty of Mathematics and Computer Science Babeş-Bolyai University 3400 Cluj, Romania [email protected], [email protected] Abstract An abstract unified theory of both monotone iterative and generalized quasilinearization methods is presented for operator equations of coincidence type in ordered Ban...

In this paper we describe a technique for closed formulation of an iterative operator-splitting method and embed the method in the classical exponential splitting methods. Since iterative operator splitting have been developed, an abstract framework to relate the method to other classical splitting methods is needed. Here an abstract framework considering the iterative splitting method as wavef...

We define a programming language independent transaction controller and an operator which when applied to concurrent programs with shared locations turns their behavior with respect to some abstract termination criterion into a transactional behavior. We prove the correctness property that concurrent runs under the transaction controller are serialisable. We specify the transaction controller T...

The article describes a new formal approach to model discrete stochastic processes, called observable operator models (OOMs). It is shown how hidden Markov models (HMMs) can be properly generalized to OOMs. These OOMs afford both mathematical simplicity and algorithmic efficiency, where HMMs exhibit neither. The observable operator idea also leads to an abstract, information-theoretic represent...

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