Riesz did some of the fundamental work in developing functional analysis and his work has had a number of important applications in physics. He established the spectral theory for boundedsymmetric operators in a form very much like that now regarded as standard.[3] He also made many contributions to other areas including ergodic theory, topology[6] and he gave an elementary proof of the mean ergodic theorem.
He had an uncommon method of giving lectures: he entered the lecture hall with an assistant and a docent. The docent then began reading the proper passages from Riesz's handbook and the assistant wrote the appropriate equations on the blackboard—while Riesz himself stood aside, nodding occasionally.[7]
The Swiss-American mathematician Edgar Lorch spent 1934 in Szeged working under Riesz and wrote a reminiscence about his time there, including his collaboration with Riesz.[4]
The corpus of his bibliography was compiled by the mathematician Pál Medgyessy.[8]
^W. J. Thron, Frederic Riesz' contributions to the foundations of general topology, in C.E. Aull and R. Lowen (eds.), Handbook of the History of General Topology, Volume 1, 21-29, Kluwer 1997.
^János Horváth: A Panorama of Hungarian Mathematics in the Twentieth Century, Volume 1, Springer, 2006 [2]
^Frederic Riesz made significant suggestions as to how the axiomatic foundations of general topology might be formulated... Unfortunately they were generally overlooked at that time and their importance was appreciated only after they were rediscovered much later... He lost interest in General Topology after 1908 and never elaborated any of the promising ideas he had put forward, Thron, cit.
^Wróblewski, Andrzej Kajetan (September 2008). "Czyściec, niebo i piekło". Wiedza i Życie: 65.
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