using the hyers-ulam-rassias stability method, weinvestigate isomorphisms in banach algebras and derivations onbanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}moreover, we prove the hyers-ulam-rassias stability of homomorphismsin banach algebras and of derivations on banach ...

In this paper, we prove that the entropy dimension of a frame spectral measure is superior than or equal to Beurling its spectrum.

We prove L estimates for the maximal Riesz transform in terms of the Riesz transform itself, for 1 < p ≤ ∞. We show that the corresponding weak L1 estimate fails for the maximal Riesz transform, but surprisingly does hold for the maximal Beurling transform.

A Beurling generalized number system is constructed having integer counting function NB(x) = κx + O ( x ) with κ > 0 and 1/2 < θ < 1, whose prime counting function satisfies the oscillation estimate πB(x)= li(x)+ ( x exp (−c√log x), and whose zeta function has infinitely many zeros on the curve σ = 1 − a/ log t , t ≥ 2, and no zero to the right of this curve, where a is chosen so that a > (4/e)...

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

We construct Boolean-valued term models and describe their universal properties. The underlying set of these models consists of the terms of the underlying language, while formulae are interpreted in the Lindenbaum-Tarski algebra of open formulae. Subspaces of the Stone space of the Lindenbaum-Tarski algebra of open formulae are shown to be homeomorphic to spaces of enumerated models models equ...

We study the concept of finitary formal topology, a point-free version of a topological space with a basis of compact open subsets. The notion of finitary formal topology is defined from the perspective of the Basic Picture (introduced by the second author) and thus it is endowed with a binary positivity relation. As an application, we prove a constructive version of Stone’s representation theo...

We discuss the most common types of weight functions in harmonic analysis and how they occur in time-frequency analysis. As a general rule, submultiplicative weights characterize algebra properties, moderate weights characterize module properties, Gelfand-Raikov-Shilov weights determine spectral invariance, and Beurling-Domar weights guarantee the existence of compactly supported test functions.