BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Filippo De Mari (Università di Genova) DTSTART:20210630T160000Z DTEND:20210630T170000Z DTSTAMP:20260423T021302Z UID:HAeS/18 DESCRIPTION:Title: Vi ews on the Radon Transform\nby Filippo De Mari (Università di Genova) as part of Harmonic analysis e-seminars\n\n\nAbstract\nI will recall and introduce some of the many existing Radon transforms\, focusing in particu lar on the setup of $G$-dual pairs $(X\,\\Xi)$ introduced by Helgason more than fifty years ago\, where $G$ is a locally compact group that acts tr ansitively both on $X$ and $\\Xi$. \nI will then present some results obta ined in collaboration with G. S. Alberti\, F. Bartolucci\, E. De Vito\, M . Monti and F. Odone which bring into play (square integrable) representat ions. If the functions to be analyzed live on $X$ and the quasi regular r epresentation of $G$ on $L^2(X)$ and $L^2(\\Xi)$ are square integrable\, t hen it is possible to write a nice inversion formula for the Radon transfo rm associated to the families of submanifolds of $X$ that are prescribed b y the object $\\Xi$ which is dual to $X$. This formula hinges on a unitari zation of the Radon transform that may be proved in a rather general setup if the quasi regular representations of $G$ on $L^2(X)$ and $L^2(\\Xi)$ are irreducible\, and on an intertwining property of the Radon transform. The former result is inspired by work of Helgason. Some examples are disc ussed\, mostly the guiding case related to shearlets that points in the di rection of possible practical inversion techniques.\n LOCATION:https://researchseminars.org/talk/HAeS/18/ END:VEVENT END:VCALENDAR