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22 results on '"Abreu Blaya, R."'

3. On the solvability of the jump problem in Clifford analysis

Author

Abreu-Blaya, R., Bory-Reyes, J., and Kats, B.A.

Subjects
Algebra -- Analysis, Mathematics
Abstract

Let [OMEGA] be a bounded open and oriented connected subset of [R.sup.n] which has a compact topological boundary [GAMMA], let C be the Dirac operator in [R.sup.n], and let [R.sub.0,n] be the Clifford algebra constructed over the quadratic space [R.sup.n]. An [R.sub.0,n]-valued smooth function f: [OMEGA] [right arrow] [R.sub.0,n] in [OMEGA] is called monogenic in [OMEGA] if Df = 0 in [OMEGA]. The aim of this paper is to present the most general condition on [GAMMA] obtained so far for which a Holder continuous function f can be decomposed as [F.sup.+] - [F.sup.-] = f on [GAMMA], where the components [F.sup.[+ or -]] are extendable to monogenic functions in [[OMEGA].sup.[+ or -]] with [[OMEGA].sup.+] := [OMEGA], and [[OMEGA].sup.-] := [R.sup.n]\([OMEGA] [union] [GAMMA]), respectively., CONTENTS 1. Introduction 2. Preliminaries. Clifford Algebras and Monogenic Functions 3. Approximate Dimension and d-Summability 4. The Jump Problem for Monogenic Functions References 1. Introduction The Clifford algebra is an [...]

Published
2013

8. Hölder Norm of a Fractal Hilbert Transform in Douglis Analysis

Author

Abreu-Blaya, R., Bory-Reyes, J., and Vilaire, J. M.

Subjects
Hyperanalytic functions, 30E25, 45E05, Hölder functions, fractal dimensions, 30E20, Whitney decomposition, Hilbert transform
Abstract

We establish an upper bound for the norm of a fractal Hilbert transform in the space of Hölder analytic functions in the sense of Douglis.

Published
2014

9. On the Hilbert formulas on the unit circle for α-hyperholomorphic function theory.

Author

Bory Reyes, J., Abreu Blaya, R., Pérez-de la Rosa, M. A., and Schneider, B.

Subjects
*HILBERT functions, *SINGULAR integrals, *GRAPH theory, *BOUNDARY value problems, *MATHEMATICAL models
Abstract

We obtain some analogues of the Hilbert formulas on the unit circle for -hyperholomorphic function theory in for being a complex quaternionic number. The obtained formulas relate a pair of components of the boundary value of an -hyperholomorphic function in the unit disc with the other pair of components and, hence, being analogous to the case of the theory of functions of one complex variable. [ABSTRACT FROM AUTHOR]

Published
2018
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10. Integration over non-rectifiable curves and Riemann boundary value problems

Author

Abreu-Blaya R., Bory-Reyes J., and Kats B.

Subjects
Cauchy integral, Douglis algebra, Fractional dimension, Riemann boundary value problem, Non-rectifiable curve
Abstract

In this paper we introduce an alternative way of defining the curvilinear Cauchy integral over non-rectifiable curves in the case of complex functions of one complex variable. Especially the jump behavior on the boundary is considered. As an application, solvability conditions of the Riemann boundary value problem are derived on very weak conditions to the boundary. Besides the complex case the consideration can be extended to the theory of Douglis algebra valued functions. © 2011 Elsevier Inc.

Published
2011

14. Boundary value problems for Dirac operators and Maxwell's equations in fractal domains.

Author

Abreu Blaya, R., Ávila Ávila, R., and Bory Reyes, J.

Subjects
*BOUNDARY value problems, *DIRAC operators, *MAXWELL equations, *ELECTROMAGNETIC fields, *FRACTAL analysis, *GEOMETRIC function theory
Abstract

Some boundary value problems are solved for time-harmonic electromagnetic fields on fractal domains, in the framework of exploiting hypercomplex function theory. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Published
2015
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19. On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

Author

Bory Reyes J., Abreu Blaya R., Rodríguez Dagnino R., Kats B., Bory Reyes J., Abreu Blaya R., Rodríguez Dagnino R., and Kats B.

Abstract

© 2018, Springer International Publishing AG, part of Springer Nature. The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R 2 . Our analysis is based on a suitable operator calculus.

20. Integration over non-rectifiable curves and Riemann boundary value problems

Author

Abreu-Blaya R., Bory-Reyes J., Kats B., Abreu-Blaya R., Bory-Reyes J., and Kats B.

Abstract

In this paper we introduce an alternative way of defining the curvilinear Cauchy integral over non-rectifiable curves in the case of complex functions of one complex variable. Especially the jump behavior on the boundary is considered. As an application, solvability conditions of the Riemann boundary value problem are derived on very weak conditions to the boundary. Besides the complex case the consideration can be extended to the theory of Douglis algebra valued functions. © 2011 Elsevier Inc.

21. Integration over non-rectifiable curves and Riemann boundary value problems

Author

Abreu-Blaya R., Bory-Reyes J., Kats B., Abreu-Blaya R., Bory-Reyes J., and Kats B.

Abstract

In this paper we introduce an alternative way of defining the curvilinear Cauchy integral over non-rectifiable curves in the case of complex functions of one complex variable. Especially the jump behavior on the boundary is considered. As an application, solvability conditions of the Riemann boundary value problem are derived on very weak conditions to the boundary. Besides the complex case the consideration can be extended to the theory of Douglis algebra valued functions. © 2011 Elsevier Inc.

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