Speaker: Zivorad Tomovski, Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacky University Olomouc, Czech Republic

Time : 15:00 - 16:00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

Zoom link : https://sissa-it.zoom.us/j/85862661154?pwd=BHBlAA2Q5NfqEmq5PvG0HIUQpi4XA6.1

• Meeting ID : 858 6266 1154
• Passcode : 090525

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords:  Superadditive functions, Mittag-Leffler function, Fractional moment generating function, Sidon inequality, Sidon–Telyakovskii class, Trigonometric series, Weyl fractional derivative, L1 convergence

Abstract: Using the concept of superadditive functions, we present some inequalities for one parameter Mittag-Leffler functions. Application is given to probability moment generating functions of fractional order. The second part of the talk is regarding L¹ estimates of fractional derivatives of trigonometric series when the Fourier coefficients belongs to the Sidon--Telyakovski class.

Biography: Currently Zivorad Tomovski is a full time professor of Applied Analysis and Probability at the Department of Mathematical Analysis and Applications of Mathematics, Faculty of Sciences, Palack\'y University Olomouc, Czech Republic. His PhD was conducted in 2000 under the direction of Prof. S. A. Telyakovskii of the Steklov Mathematical Institute, Moscow, in the area of Approximation Theory and Fourier Analysis. He received the PhD degree at the Faculty of Mathematics and Natural Sciences, Ss. Cyril and Methodius University Skopje in 2000, where in 2010 he received a Full Professorship position and in 2012 he was awarded best scientist. In 2022, he received Habilitation in Applied Mathematics at Ostrava University. His recent research has been focused on the development and the analysis of computational tools for Mathematical modelling of anomalous diffusion, wave propagation and fractional PDE with stochastic analysis. He has published more than 100 papers in international journals of mathematics and physics with impact factor, and 2 Springer monographs, available online on his RG profile: https://www.researchgate.net/profile/Zivorad_Tomovski

Tomovski has been a principal investigator/co-investigator in numerous international research projects and grants, supported by DAAD-Germany, NWO-Holland, Einstein Foundation Research Program-Berlin, Austrian Agency for Research OeAD-GmbH, Croatian Ministry of Sciences and Sports, Macedonian Ministry of Sciences and Education, NEWFELPRO- Marie Curie FP7 program 2014-2016 and Bilateral grant GACR-DFG. 

Bibliography

[1] Z. Tomovski, R. Metzler, S. Gerhold, Fractional characteristic functions, and a fractional calculus approach for moments of random variables, Fractional Calculus andApplied Analysis, Vol.25 (3) (2022). 
[2] S. Iqbal, J. Pecaric, Z. Tomovski, Analytical Inequalities in fractional calculus (2020), Lambert Academic Publishing book, 307 pp.
[3] Z. Tomovski, An extension of the Sidon-Fomin type inequality and its applications, Math. Inequal. Appl. 4 (2), (2001) 231-238.
[4] Z. Tomovski, A note on two inequalities of Telyakovskii type, RGMIA, Research Report Collection, 4 (1), Article 7, (2001) (electronic) (URL: http://melba.vu.edu.au/ rgmia/v4n1.html).
[5] Z. Tomovski, A note on the Leindler’s class, International Workshop of INEQUALITIES in Temisoara, Romania in Jule, 2001; Math. Ineq. Appl.5 (3), (2002), 505-509
[6] Z. Tomovski , Some results on L1 approximation of the r-th derivative of Fourier series, J. Inequal. Pure Appl. Math., 4 (1) (2002), Article 10, 11 pp. (electronic).
[7] Z. Tomovski, Some New Integrability Classes of Fourier Coefficients, Constructive Theory of Functions, Varna 2002, DARBA, Sofia, 2003, pp.433-439.
[8] S.A Telyakovskii, On a sufficient condition of Sidon for the Integrability of trigono- metric series, Math. Notes, 14 (1973), pp. 742-748
[9] L. Leindler, On the utility of Telyakovskii class, JIPAM 2 (3) (2001).