Time-Frequency Methods for Operators and Function Spaces
Public support
Provider
Ministry of Education, Youth and Sports
Programme
Programme for Funding Multilateral Scientific and Technological Cooperation Projects in the Danube Region
Call for proposals
Program pro financování projektů mnohostranné vědeckotechnické spolupráce v Podunajském regionu (SMSM20168X001)
Main participants
Univerzita Karlova / Matematicko-fyzikální fakulta
Contest type
VS - Public tender
Contract ID
MSMT-3375/2017-1
Alternative language
Project name in Czech
Časově-frekvenční metody pro operátory a prostory funkcí
Annotation in Czech
Quite a large number of problems in mathematical analysis require to look at linear operators between function spaces. This is obvious for diferential operators, which are typically treated as a mapping between Sobolev spaces. The perfect situation are elliptic partial diferential operators, because they can be viewed as an isomorphism between two classical spaces of this type, thus opening the way to an exact characterization of the Laplace equation. Just to give another example we know that the Hilbert space L2(Rd) is perfectly well suited in order to describe the behavior of the Fourier transform, thanks to Plancherel's Theorem. For engineers the space C0(Rd) of continuous, bounded functions vanishing at infinity (with the sup-norm) may be considered the natural domain for the description of translation invariant operators (they can be identified with convolution operators induced by bounded measures). In the context of Gabor Analysis however modulation spaces Ms p;q(Rd) turned out to be much better suited, in particular the Segal algebra S0(Rd) and its dual (corresponding to the cases p = 1 = q and p = 1 = q, respectively). The proposed network is supposed to develop an approach to problems concerning operators and function spaces from a time-frequency point of view, and to explore the advantages of such a perspective. The governing principle for such an approach will be idea of Conceptual Harmonic Analysis" as it has been promoted by Hans G. Feichtinger at NuHAG in Vienna for some time.
Scientific branches
R&D category
ZV - Basic research
CEP classification - main branch
BA - General mathematics
CEP - secondary branch
—
CEP - another secondary branch
—
OECD FORD - equivalent branches <br>(according to the <a href="http://www.vyzkum.cz/storage/att/E6EF7938F0E854BAE520AC119FB22E8D/Prevodnik_oboru_Frascati.pdf">converter</a>)
10101 - Pure mathematics
Completed project evaluation
Provider evaluation
U - Uspěl podle zadání (s publikovanými či patentovanými výsledky atd.)
Project results evaluation
This project was being realized in the framework of the MOBILITY Activity that aims primarily on establishing and strenghtening ties with foreign research institutions. The control of particular outputs is not implemented by the evalution committee, but the correctness of allocated finances and the adequacy of their use are checked.
Solution timeline
Realization period - beginning
Jan 1, 2017
Realization period - end
Dec 31, 2018
Project status
U - Finished project
Latest support payment
Feb 28, 2018
Data delivery to CEP
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data delivery code
CEP19-MSM-8X-U/01:1
Data delivery date
Jun 18, 2019
Finance
Total approved costs
300 thou. CZK
Public financial support
300 thou. CZK
Other public sources
0 thou. CZK
Non public and foreign sources
0 thou. CZK