BEGIN:VCALENDAR VERSION:2.0 PRODID:-//wp-events-plugin.com//7.2.3.1//EN TZID:Europe/Paris X-WR-TIMEZONE:Europe/Paris BEGIN:VEVENT UID:8311@i2m.univ-amu.fr DTSTART;TZID=Europe/Paris:20140903T093000 DTEND;TZID=Europe/Paris:20140903T153000 DTSTAMP:20241120T210332Z URL:https://www.i2m.univ-amu.fr/evenements/computational-time-frequency-an d-coorbit-theory-anr-metason-morlet-chair-hans-georg-feichtinger/ SUMMARY:Workshop (CIRM\, Luminy\, Marseille): Computational Time-Frequency and Coorbit Theory (ANR MétaSon\, Morlet Chair - Hans-Georg Feichtinger) DESCRIPTION:Workshop: \n\n\n\n\n CIRM - Jean-Morlet Chair \n Hans-Georg Fei chtinger\n&\; Bruno Torresani\n\nTime-Frequency Analysis and Coorbit Th eory​\n\n\n 2015 - Semester 2 \n\n\n\n\n\n\n\n\n\n\n\n\n\n\nOTHER EVENTS \n\nOpening Day / Journée thématique\n3 September 2014\nFRUMAM (CNRS\, Université Aix-Marseille)\n\n 9h45: coffee\, opening.\n 10h15: Hans- Georg FEICHTINGER (NuHaG\, Department of Mathematics\, University of Vienn a\, Austria): Function Spaces and Harmonic Analysis.\nIt is one of the fa cts of life that operators have certain mapping properties (e.g. the Fouri er transform\, the differentiation operator\, certain convolution operator s) and that it needs a repertoire of function spaces in order to properly describe the mapping properties of the different operators. New operators or classes of operators often initiate to introduction or great interest i n new families of spaces. Interpolation theory provides good tools to view such spaces as families and conclude from mapping properties of operators ``at the limiting cases of the parameter space’’ to the general situa tion (one may think of the Hausdorff Young theorem).\nOne of the goals of this presentation was a view on Besov spaces\, viewed as generalized Lipsc hitz spaces\, or as spaces characterized by dyadic decomposition of the Fo urier domain\, or finally as coorbit spaces with respect to the canonical representation of the ax+b-group on the Hilbert space L^2(R).\n 11h00: H artmut FÜHR (Lehrstuhl A für Mathematik\, RWTH Aachen\, FRG): Continuo us Wavelet Analysis in Higher Dimensions.\nThe continuous wavelet transfor m\, introduced by Grossmann\, Morlet and Paul for one-dimensional signals\ , generalizes to higher dimensions in many distinct ways. Initial higher-d imensional analogs were based on the similitude groups\, more recent const ructions use anisotropic alternatives such as the shearlet.\nIn the talk F ühr reviewied the group-theoretic construction of these systems. The appr oximation-theoretic properties of the various wavelet systems can be studi ed in a very general unified manner using coorbit theory. For most of the interesting properties of the generalized wavelet transform\, a proper und erstanding of the dual action underlying the wavelet system is crucial.\n 12h00: lunch break.\n 14h00: Karlheinz GRÖCHENIG (NuHaG\, Department o f Mathematics\, University of Vienna\, Austria): Bergman Spaces on the Un it Ball and Coorbit Theory.\nCoorbit theory is a general machine to define Banach spaces and to derive atomic decompositions and Banach frames. Its starting point is a (square) integrable\, irreducible unitary representati on of a locally compact group.\nFor instance\, the coorbit spaces associat ed to the group of affine translations are just the Besov space\, and the corresponding atomic decompositions are their wavelet expansions. In this talk Gröchenig explained the coorbit spaces arising from the discrete ser ies of SU(n\,1) and their atomic decompositions. The coorbits attached to these representations were the classical Bergman spaces on the unit ball i n $C^n$. The corresponding atomic decompositions were those derived by Coi fman and Rochberg with complex-analytic methods.\n(This is joint work with Jens G. Christensen and G. Olafsson).\n 14h45: Radu BALAN (Department of Mathematics and Center for Scientific Computation and Mathematical Modeli ng\, University of Maryland\, USA): Phase Retrieval using Lipschitz Conti nuous Maps.\nIn this talk Balan showed that reconstruction from magnitudes of frame coefficients (the so called "phase retrieval problem") can be pe rformed using Lipschitz continuous maps. Specifically we show that when th e nonlinear analysis map a:H ->\; R^m is injective\, with (a(x))_k = |&l t\;x\,fk>\;|^2\, where {f1\, ...\, fm} is a frame for the Hilbert space H\, then there exists a left inverse map w:R^m->\;H that is Lipschitz co ntinuous.\nAdditionally we obtain the Lipschitz constant of this inverse m ap in terms of the lower Lipschitz constant of a.\n\n\n\n\n\n\n \n\n\n\n\ n\n\n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n CATEGORIES:Manifestation scientifique,Morlet Chair Semester,Morlet Workshop END:VEVENT BEGIN:VTIMEZONE TZID:Europe/Paris X-LIC-LOCATION:Europe/Paris BEGIN:DAYLIGHT DTSTART:20140330T030000 TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST END:DAYLIGHT END:VTIMEZONE END:VCALENDAR