Eusebio Ariza Garcia

RESEARCH INTERESTS

Harmonic Analysis, Real Analysis, Clifford Analysis, Hypercomplex algebras, Wavelet theory, PDEs, Integral transforms, Mathematical disclosure, History of mathematics, mathematics education.

Scopus Publications

Parabolic Dirac operators and their fundamental solutions in parametric Clifford algebras




One—dimensional Quaternion Fourier Transform and Some Applications




One dimensional octonion Fourier Transform




ψ-weighted Cauchy-Riemann operators and some associated integral representation
Eusebio Ariza, Antonio Di Teodoro, and Carmen Judith Vanegas
National Inquiry Services Center (NISC)
Abstract In the present work we introduce a weighted Cauchy-Riemann type operator in the complex plane, where the weights are complex non-constant functions. We construct a fundamental solution for this operator where the weights are complex constant functions and orthogonal functions inspired by the idea for the construction of the Levy function proposed by Miranda (see [23]). Therefore we obtain a Cauchy-Pompeiu integral representation formula. We also present some examples of such representations when we take some particular weights.


Interior estimates in the sup-norm for a class of generalized functions with integral representations




Sufficient Conditions for First-Order Differential Operators to be Associated with a q-Metamonogenic Operator in a Clifford Type Algebra
Eusebio Ariza García, Antonio Di Teodoro, María Sapiain, and Franklin Vargas
Springer Science and Business Media LLC



First Order Differential Operators Associated to the Space of q-Monogenic Functions
Eusebio Ariza García, Antonio Di Teodoro, and Judith Vanegas
Springer Science and Business Media LLC



An Integral Representation Formula for Multi Meta- φ -Monogenic Functions of Second Class
Eusebio Ariza García and Antonio Di Teodoro
Springer Science and Business Media LLC



First Order Differential Operators Associated to the Space of Monogenic Functions in Parameter-Depending Clifford Algebras
Eusebio Ariza, Judith Vanegas, and Franklin Vargas
Springer Science and Business Media LLC



Cauchy–Pompeiu formula for multi-meta-weighted-monogenic functions of first class
Eusebio Ariza García and Antonio Di Teodoro
Springer International Publishing



Fundamental Solutions for Second Order Elliptic Operators in Clifford-Type Algebras
Eusebio Ariza, Antonio Di Teodoro, Adrián Infante, and Judith Vanegas
Springer Science and Business Media LLC



Interior L<inf>p</inf>-Estimates for Functions in Clifford Type Algebras
Eusebio Ariza, Yanett Bolívar, Luis Mármol, and Judith Vanegas
Springer Science and Business Media LLC



Multi Mq-monogenic function in different dimension
Eusebio Ariza and Antonio Di Teodoro
Springer International Publishing



Hartog's Type Extension Theorem in Some Piecewise Constant Structure Relations For Metamonogenic Functions of First Order
Eusebio Ariza and Antonio Di Teodoro
Springer Science and Business Media LLC

RECENT SCHOLAR PUBLICATIONS

ψ-weighted Cauchy-Riemann operators and some associated integral representation
E Ariza, A Di Teodoro, CJ Vanegas
Quaestiones Mathematicae 43 (3), 335-360 2020



Sufficient Conditions for First-Order Differential Operators to be Associated with a q-Metamonogenic Operator in a Clifford Type Algebra
E Ariza Garca, A Di Teodoro, M Sapiain, F Vargas
Computational Methods and Function Theory 17, 211-236 2017



First Order Differential Operators Associated to the Space of q-Monogenic Functions
E Ariza Garca, A Di Teodoro, J Vanegas
Advances in Applied Clifford Algebras 27, 135-147 2017



Sufficient conditions for first-order differential operators to be associated with a q-metamonogenic operator in a Clifford type algebra
E Ariza, A Di Teodoro, M Sapiain, F Vargas
Comput. Methods Funct. Theory 17, 211-236 2017



First order differential operators associated to the space of monogenic functions in parameter-depending Clifford algebras
E Ariza, J Vanegas, F Vargas
Advances in Applied Clifford Algebras 26 (1), 13-29 2016



Fundamental solutions for second order elliptic operators in Clifford-type algebras
E Ariza, A Di Teodoro, A Infante, J Vanegas
Advances in Applied Clifford Algebras 25, 527-538 2015



Interior L _p -Estimates for Functions in Clifford Type Algebras
E Ariza, Y Bolvar, L Mrmol, J Vanegas
Advances in Applied Clifford Algebras 25, 271-282 2015



PROBLEMAS DE VALORES INICIALES Y REPRESENTACIONES INTEGRALES EN ANALISIS DE CLIFFORD
E Ariza, A Di Teodoro
Acta Cientıfica Venezolana 65 (4), 225-233 2014



Multi M_q-monogenic Function in Different Dimension
E Ariza, A Di Teodoro
Hypercomplex Analysis: New Perspectives and Applications, 61-73 2013



Hartog’s Type Extension Theorem in Some Piecewise Constant Structure Relations For Metamonogenic Functions of First Order
E Ariza, A Di Teodoro
Advances in Applied Clifford Algebras 23, 561-576 2013



TEOREMAS DE EXTENSION TIPO HARTOGS EN ANALISIS DE CLIFFORD.
E Ariza
2011



Teorema de extensin para funciones multi-monognicas en lgebras parametrizadas
E Ariza, CJ Vanegas
Boletın de la Asociacin Matemtica Venezolana, 5 2011



Past and Future Directions in Hypercomplex and Harmonic Analysis
E Ariza, A Di Teodoro, F Vargas

MOST CITED SCHOLAR PUBLICATIONS

First order differential operators associated to the space of monogenic functions in parameter-depending Clifford algebras
E Ariza, J Vanegas, F Vargas
Advances in Applied Clifford Algebras 26 (1), 13-29 2016
Citations: 6



ψ-weighted Cauchy-Riemann operators and some associated integral representation
E Ariza, A Di Teodoro, CJ Vanegas
Quaestiones Mathematicae 43 (3), 335-360 2020
Citations: 4



Fundamental solutions for second order elliptic operators in Clifford-type algebras
E Ariza, A Di Teodoro, A Infante, J Vanegas
Advances in Applied Clifford Algebras 25, 527-538 2015
Citations: 4



Interior L _p -Estimates for Functions in Clifford Type Algebras
E Ariza, Y Bolvar, L Mrmol, J Vanegas
Advances in Applied Clifford Algebras 25, 271-282 2015
Citations: 3



Teorema de extensin para funciones multi-monognicas en lgebras parametrizadas
E Ariza, CJ Vanegas
Boletın de la Asociacin Matemtica Venezolana, 5 2011
Citations: 3



Sufficient conditions for first-order differential operators to be associated with a q-metamonogenic operator in a Clifford type algebra
E Ariza, A Di Teodoro, M Sapiain, F Vargas
Comput. Methods Funct. Theory 17, 211-236 2017
Citations: 2



Multi M_q-monogenic Function in Different Dimension
E Ariza, A Di Teodoro
Hypercomplex Analysis: New Perspectives and Applications, 61-73 2013
Citations: 2



PROBLEMAS DE VALORES INICIALES Y REPRESENTACIONES INTEGRALES EN ANALISIS DE CLIFFORD
E Ariza, A Di Teodoro
Acta Cientıfica Venezolana 65 (4), 225-233 2014
Citations: 1