Reference : Solvability of invariant systems of differential equations on the hyperbolic plane

	Document type :	Scientific Presentations in Universities or Research Centers : Scientific presentation in universities or research centers
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/51186

Title :	Solvability of invariant systems of differential equations on the hyperbolic plane
Language :	English
Author, co-author :	Palmirotta, Guendalina [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Publication date :	28-Jun-2022
Audience :	International
Event name :	Oberseminar "Geometrische Analysis und Zahlentheorie"
Event date :	28.06.22
Event organizer :	Christian Arends and Jan Frahm
Event place (city) :	Paderborn
Event country :	Germany
Abstract :	[en] In the Euclidean case, it is well-known, by Malgrange and Ehrenpreis, that linear differential operators with constant coefficients are solvable. However, what happens, if we genuinely extend this situation and consider systems of linear invariant differential operators, is still solvable? In case of Rn (for some positive integer n), the question has been proved mainly by Hörmander. We will show that this remains still true for Riemannian symmetric spaces of non-compact type X = G/K. More precisely, we will present a possible strategy to solve this problem by using the Fourier trans- form and its Paley-Wiener(-Schwartz) theorem for (distributional) sections of vector bundles over X. We will get complete solvability for the hyperbolic plane H2 = SL(2, R)/SO(2) and beyond. This work was part of my doctoral dissertation supervised by Martin Olbrich.
Funders :	Fonds National de la Recherche - FnR
Name of the research project :	PRIDE15/10949314/GSM
Target :	Researchers
Permalink :	http://hdl.handle.net/10993/51186
Other URL :	https://math.uni-paderborn.de/ag/arbeitsgruppe-spektralanalysis/forschung/geometrische-analysis-und-zahlentheorie#:~:text=In%20diesem%20gemeinsamen%20Oberseminar%20der,der%20Zahlentheorie%20pr%C3%A4sentiert%20und%20diskutiert.

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