Information
Abstract
The project is devoted to two central fields of modern mathematical analysis, operator related function theory and time–frequency analysis, and the profound interplay between these two areas, which to a large extent are mutually complementary. Complex analysis, which in the first half of the previous century was mainly a purely theoretical discipline, is now a powerful tool in harmonic and functional analysis, probability theory as well as in applied areas such as, for example, control theory and information theory. Time–frequency analysis originated within quantum mechanics and signal analysis; it has grown into an independent mathematical discipline, intertwined with parts of harmonic analysis, combinatorial and geometrical analysis, representation theory, pseudodifferential operators, and C*algebras. Methods, approaches, and – perhaps even more importantly – the philosophy of time – frequency analysis allow one to reexamine known results, discover new unexplored areas in classical function theory, and also to establish surprising and profound relations between problem arising in areas of mathematics that are seemingly distant from each other. One of the most fascinating examples of such interaction is the socalled Feichtinger conjecture, which arose from problems in time–frequency analysis. A few years ago, the Feichtinger conjecture was shown to be equivalent to longstanding unresolved fundamental conjectures in combinatorial analysis (the paving conjecture) and mathematical physics (the Kadison–Singer conjecture). One possible way of attacking this problem is based on methods from operator related function theory, such as spaces of analytic functions and sampling theory. Another example of similar remarkable interaction between subfields of mathematical analysis is found in scattering theory, which combines methods of mathematical physics, operator related function theory, partial differential equations, and harmonic analysis. This field originated in the study of basic physical phenomena and finds direct applications for example in nanotechnology. The project is aimed to promote collaboration and interaction on these and other similar topics between experts in operator related function theory and time–frequency analysis, with a view to the relevance for engineering and physical sciences. Such interplay will enrich both disciplines and lead to a deeper understanding of important challenges, including the two topics mentioned above. More specifically, the project is expected to lead to new advances in areas such as spaces of analytic functions, spectral function theory, potential theory, Gabor analysis, as well as in applications to scattering theory (in particular, scattering on quantum graphs), partial differential operators, and geometrical analysis.
Fellows

Belov, YuriiPostdoctoral Fellow St.Petersburg State University

Borichev, AlexanderProfessor AixMarseille University

Eikrem, Kjersti SolbergPh. D. Candidate Norwegian University of Science and Technology

Grepstad, SigridDr. Norwegian University of Science and Technology

Gröchenig, KarlheinzDr. University of Vienna

Lacey, Michael ThoreauProfessor Georgia Institute of Technology

Malinnikova, EugeniaAssociate Professor Norwegian University of Science and Technology

Montes Rodriguez, AlfonsoProfessor University of Seville

Ortega Cerdá, Joaquim University of Barcelona

Perfekt, KarlMikaelPh. D. Candidate Lund University

Poltoratski, AlexeiProfessor Texas A&M University

Queffelec, MartineAssistant Professor Lille University of Science and Technology

Queffelec, HervéProfessor Em. Lille University of Science and Technology

Saksman, EeroProfessor University of Helsinki

Sodin, MikhailProfessor Tel Aviv University

Vähäkangas, AnttiPostdoctoral Fellow University of Helsinki

Weber, Michel Jeon GeorgesDirector University of Strasbourg
Previous events

20 Jun 2013(all day)Turrent Room, CAS, Oslo Turrent Room, CAS, Oslo

06 May  10 May 2013(all day)Trondheim Trondheim

30 Apr 2013(all day)University of Oslo University of Oslo

25 Mar  26 Mar 2013(all day)AixMarseille University, France AixMarseille University, France

11 Feb  15 Feb 2013

21 Aug  24 Aug 2012