In this article, we introduce and study a family of compatible functions in Hilbert algebras which in the case of Heyting algebras agree with the frontal operators given by Esakia (2006, J. Appl. Non-Class. Log., 16, ...

Consider the discrete quadratic phase Hilbert Transform acting on $\ell^{2}(\mathbb{Z})$ finitely supported functions $$ H^{\alpha} f(n) : = \sum_{m \neq 0} \frac{e^{i\alpha m^2} f(n - m)}{m}. $$ We prove that, ...

Consider the discrete quadratic phase Hilbert Transform acting on $\ell^{2}(\mathbb{Z})$ finitely supported functions $$ H^{\alpha} f(n) : = \sum_{m \neq 0} \frac{e^{i\alpha m^2} f(n - m)}{m}. $$ We prove that, ...

In this work we study the basic concepts of functional analysis, such as metric spaces, normed spaces, Banach spaces, as well as some topological notions, linear functional, inner product and Hilbert spaces. Finally, we ...

The main purpose of this paper is to get a similar relation to Hilbert's formula on the real line, for the case of -hiperholomor c functions H valued. It takes as guideline a generalization of Hilbert's formula on the ...

In this paper, a definition of the Hilbert transform operating on Colombeau's temperated generalized functions is given. Similar results to some theorems that hold in the classical theory, or in certain subspaces of Schwartz ...