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Mathematics Webinar | Recent Advances on Approximation Theory

10 Nov 2022, 09:00 (CET)

Approximation Theory, Special Functions, Orthogonal Polynomials, Fractional Calculus
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Welcome from the Chair

3rd Mathematics Webinar

Recent Advances on Approximation Theory

The approximation is the basis of all mathematical procedures, since the exact solutions of the problems of the applied sciences are limited to a negligible number of cases. The same real numbers, not rational, they can be conceived only for the possibility of assigning for them some approximations by default and by excess, with a consequent estimate of the error. The modern theory of approximation can be traced back to P.L. Chebyshev. His first work on approximation: "Théorie des mécanismes connus sous le nom de parallélogrammes" (1854) and the following: "Sur les questions de minima qui se rattachent à la représentation approximative des functions" (1859), began 40 years of research on approximation in connection with the theory of mechanisms. Orthogonal polynomials and special functions represent a crucial tool for approaching the modern theory of approximation. The orthogonality property is certainly the most important one to use in approximation problems, since it allows to avoid the numerical instability that occurs using the Hilbert matrix. It has been shown that the pseudo-Chebyshev functions verify this property (in the same interval and with the same weights of the corresponding classical polynomials). It is not necessary to remember the importance of the numerous families of polynomials and special functions that come used in the solutions of the most diverse problems of mathematical physics. Among these, they have great relevance the Bessel functions, recently linked to Legendre polynomials. The analysis of fractional calculus through the concepts and formalism of some class of orthogonal polynomials (in particular the Hermite polynomials) had an important development, also in relation to the large interest that this research sector has had in recent years.

Date: 10 November 2022

Time: 9:00 am CET | 3:00 am EST | 1:30 pm IST | 4:00 pm CST Asia

Webinar ID: 856 3178 1191

Webinar Secretariat:


Section of Mathematics Luciano Modica, Uninettuno University, Rome, Italy

Clemente Cesarano is associate professor of Numerical Analysis at the Section of Mathematics -Uninettuno University, Rome Italy; he is the coordinator of the doctoral college in Technological Innovation Engineering, coordinator of the Section of Mathematics, vice-dean of the Faculty of Engineering, president of the Degree Course in Management Engineering, director of the Master in Project Management Techniques, and coordinator of the Master in Applied and Industrial Mathematics. He is also a member of the Research Project “Modeling and Simulation of the Fractionary and Medical Center”, Complutense University of Madrid (Spain) and head of the national group from 2015, member of the Research Project (Serbian Ministry of Education and Science) “Approximation of Integral and Differential Operators and Applications”, University of Belgrade (Serbia) and coordinator of the national group from 2011-), a member of the Doctoral College in Mathematics at the Department of Mathematics of the University of Mazandaran (Iran), expert (Reprise) at the Ministry of Education, University and Research, for the ERC sectors: Analysis, Operator algebras and functional analysis, Numerical analysis. Clemente Cesarano is Honorary Fellows of the Australian Institute of High Energetic Materials, affiliated with the National Institute of High Mathematics (INdAM), is affiliated with the International Research Center for the “Mathematics & Mechanics of Complex Systems” (MEMOCS) - University of L’Aquila, associate of the CNR at the Institute of Complex Systems (ISC), affiliated with the “Research ITalian network on Approximation (RITA)” network as the head of the Uninettuno office, UMI member, SIMAI member.

Invited Speakers

Department of Mathematics, Anand International College of Engineering, Jaipur, India

Dr. Praveen Agarwal is an associate professor at Anand International College of Engineering, India. His major research interests include Special Functions, Fractional Calculus, Numerical Analysis, Differential and Difference Equations, Inequalities, and Fixed Point Theorems. He has published 7 research monographs and edited volumes and more than 150 publications (with almost 100 mathematicians all over the world) in prestigious national and international mathematics journals. He worked previously either as a regular faculty or as a visiting professor and scientist in universities in several countries, including India, Germany, Turkey, South Korea, UK, Russia, Malaysia and Thailand. Specially, he was awarded most respected International Centre for Mathematical Sciences (ICMS) Group Research Fellowship to work at ICMS Centre, Scotland, UK, and during 2017-18, he was awarded most respected TUBITAK Visiting Scientist Fellowship to work with at AhiEvran University, Turkey. He has been awarded by Most Outstanding Researcher-2018 (Award for contribution to Mathematics) by the Union Minister of Human Resource Development of India, Mr Prakash Javadekar in 2018. He has been invited to give plenary/keynote lectures at a number of international conferences.

Dipartimento di Matematica “Tullio Levi-Civita”, Università di Padova, Padua, Italy

Stefano De Marchi is a full professor of numerical analysis at the University of Padova, Department of Mathematics "Tullio Levi-Civita". His main research interests include multivariate approximation by polynomials and radial basis functions. He is one of the discoverers of the Padua points, the quasi-optimal set of points on the square unisolvent for polynomial interpolation of total degree. He is the author and co-author of more than 100 papers. He is the editor, among them, of BIT Numerical Mathematics, Journal of Approximation Theory, MDPI-Mathematics, and managing editor of Dolomites Research Notes on Approximation.

Section of Mathematics Luciano Modica, Uninettuno University, Rome, Italy

Paolo Emilio Ricci was Professor at the University Campus Bio-medico of Rome for several years. At present he is teacher at the UniNettuno Telematic University in Rome. In the period 1983-1992 he was Scientific director of the Journal "Rendiconti di Matematica e delle sue Applicazioni". He is Associated Editor of several international Journals (Integral Transforms and Special Functions, Georgian Mathematical Journal, Reports of Seminar of I. Vekua Institute of Applied Mathematics, Symmetry MDPI, Symmetry: Culture and Science, Growth and Form). He has attended and gave lectures in many international conferences and was the main organizer of the Symposia "Problemi attuali dell'Analisi e della Fisica Matematica", Taormina (I: 1992; II: 1998; III: 2006) and member of the Scientific and Organizing Committe of several important meetings. In 2003 he was awarded Doctor honoris causa by the Tbilisi State University and appointed as honorary professor of the I. Vekua Institute of Applied Mathematics. In 2015 he received the special prize of the Simon Stevin Institute for Geometry, (Zandvoort, The Netherlands). In March 2016 he received the "Lifetime Achievement Award" by the Science Council of India (Vijnana Parishad of India) - Society for Applied Mathematics, Bundelkhand University, (Orai, U.P., India). He is the author/coauthor of more than 280 scientific papers and author/editor of several books in the areas of pure and applied mathematics concerning the following fields: special functions, integral and discrete transforms, symbolic and umbral calculus, ordinary and partial differential equations, asymptotic analysis, quadrature rules, symmetrization problems, eigenvalues, matrix functions, and other related subjects.

Webinar Content

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Time in CET

Prof. Dr. Clemente Cesarano

Chair Introduction

9:00 - 9:10 am

Prof. Dr. Praveen Agarwal

Extended Hypergeometric Matrix Functions and Applications

9:10 - 9:30 am

Prof. Dr. Stefano De Marchi

(β, γ)-Chebyshev Functions and Points of the Interval and Some Extensions

9:30 - 9:50 am

Prof. Dr. Paolo Emilio Ricci

Bell’s Polynomials and Laplace Transform of Nested Analytic Functions

9:50 - 10:10 am


10:10 - 10:25 am

Closing of Webinar
Prof. Dr. Clemente Cesarano

10:25 - 10:30 am

Relevant SI

Guest Editors: Prof. Dr. Miklós Rontó, Prof. Dr. András Rontó, Prof. Dr. Nino Partsvania, Prof. Dr. Bedřich Půža & Prof. Dr. Hriczó Krisztián

Deadline for manuscript submissions: 28 February 2023

Guest Editor: Prof. Dr. Octav Olteanu
Deadline for manuscript submissions: 15 April 2023

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