In this paper, first we define the notion of involutive operator on bounded involutive equality algebras and by using it, we introduce a new class of equality algebras that we called it a tense like equality algebra. Then we investigate some properties of tense like equality algebra. For two involutive bounded equality algebras and an equality homomorphism between them, we prove that the tense ...

Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

We study the global hypoellipticity problem for certain linear operators in Komatsu classes of Roumieu and Beurling type on compact manifolds. present an approach by combining a characterization these spaces via eigenfuction expansions, generated elliptic operator, analysis matrix-symbols obtained expansions.

The Mergelyan and Ahlfors-Beurling estimates for the Cauchy transform give quantitative information on uniform approximation by rational functions with poles off K. We will present an analogous result for an integral transform on the unit sphere in C2 introduced by Henkin, and show how it can be used to study approximation by functions that are locally harmonic with respect to the Kohn Laplacia...

We associate to the global field K a Lax–Phillips scattering which has the property of causality if and only if the Riemann Hypothesis holds for all the abelian L–functions of K. As a Hilbert space closure problem this provides an adelic variation on a theme initiated by Nyman and Beurling. The adelic aspects are related to previous work by Tate, Iwasawa and Connes. Université de NiceSophia Ant...

The generalized Beurling–Ahlfors operator S on L(R; Λ), where Λ := Λ(R) is the exterior algebra with its natural Hilbert space norm, satisfies the estimate ‖S‖L (Lp(Rn;Λ)) ≤ (n/2 + 1)(p ∗ − 1), p∗ := max{p, p′}. This improves on earlier results in all dimensions n ≥ 3. The proof is based on the heat extension and relies at the bottom on Burkholder’s sharp inequality for martingale transforms.

Abstract. V. I. Vasyunin has introduced special sequences of step functions related to the strong Nyman-Beurling criterion that converge pointwise to 1 in [1,∞). We show here that the first and simplest such sequence considered by Vasyunin diverges in L1((1,∞), x dx), which of course precludes the L2((1,∞), x dx)-convergence needed for the Riemann hypothesis. Whether all sequences considered by...

This paper concerns a class of monotone mappings in a Hilbert space that can be viewed as a nonlinear version of the class of positive invertible operators. Such mappings are proved to be open, locally Hölder continuous, and quasisymmetric. They arise naturally from the Beurling-Ahlfors extension and from Brenier’s polar factorization, and find applications in the geometry of metric spaces and ...

In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach ...