Abstract. We use free probability techniques to compute borders of spectra of non hermitian operators in finite von Neumann algebras which arise as “free sums” of “simple” operators. To this end, the resolvent is analyzed with the aid of the Haagerup inequality. Concrete examples coming from reduced C∗-algebras of free product groups and leading to systems of polynomial equations illustrate the...

Let A be a bounded operator on a Banach space X. A scalar λ is in the spectrum of A if the operator A − λ is not invertible. Case closed. What more is there to say? As anyone with the slightest exposure to operator theory will testify, there is so much out there that no book could come close to being comprehensive. What authors do in such situations is choose a small area or topic of interest t...

T The nonlinear and linear Volterra-Fredholm ordinary integral equations arise from various physical and biological models. The essential features of these models are of wide applicable. These models provide an important tool for modeling a numerous problems in engineering and science [6, 7]. Modelling of certain physical phenomena and engineering problems [8, 9, 10, 11, 12] leads to two-dimens...

In this paper, we prove the existence and uniqueness of squaremean asymptotically almost automorphic mild solution of a class of partial nonlocal neutral stochastic functional integro-differential equations with resolvent operators in a real separable Hilbert space. An example illustrating our main result is given.

In this paper resolvent estimates for Abel integral operators are provided. These estimates are applied to deduce regularizing properties of Lavrentiev's m-times iterated method as well as iterative schemes ? with the discrepancy principle as corresponding parameter choice or stopping rule, respectively for solving the corresponding Abel integral equations of the rst kind.

In this paper, an α-resolution method for a set of lattice-valued Horn generalized clauses is established in lattice-valued propositional logic systemL P(X) based on lattice implication algebra. Firstly, the notions of lattice-valued Horn generalized clause, normal lattice-valued Horn generalized clause and unit latticevalued Horn generalized clause are given in L P(X). Then, the α-resolution o...

Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing resolvent modes with more than one inhomogeneous spatial coordinate remains computationally expensive. In this two-part paper, we show how efficient accurate approximations can be obtained using well-...