[NOVA Math] Seminar of Analysis

The Center of Mathematics and Applications (NOVA Math), promote the Seminar of Analysis with the title: “Fredholm theory for Wiener-Hopf integral operators on Orlicz spaces”.  Márcio Valente (NOVA FCT, NOVA Math) is the speaker.

Abstract: We extend the Fredholm criteria for Wiener-Hopf operators with continuous symbols on the Lebesgue space L_p(ℝ⁺), _p∈(1,∞), obtained by Roland Duduchava in the late 1970s, to the setting of reflexive Orlicz spaces LΦ(ℝ⁺). Following this, we formulate a conjecture which seeks to refine this result by removing the reflexivity assumption.

After this, we introduce the algebra of piecewise continuous symbols and obtain some preliminary results which in turn will lead towards the rediscovery of the Fredholm criteria for Wiener-Hopf operators with piecewise continuous symbols on the Lebesgue space L_p(ℝ⁺), _p∈(1,∞), which was also obtained by Roland Duduchava. Finally, a conjecture is presented as we try to extend this result to the setting of Orlicz spaces.

Keywords: Fourier multiplier, Wiener-Hopf operator, Fredholm criteria, Orlicz space.

Thursday, 4 July 2024, from 11h00 to 11h50.

Zoom link: https://videoconf-colibri.zoom.us/j/92219333954?pwd=BrsfbKDEVGddzLiWbdEpoEex4NSawC.1