English
Continuous (semi-)frames revisited
Multi angle
Auteurs : Antoine, Jean-Pierre (Auteur de la Conférence)
CIRM (Editeur )
42C15 - General harmonic expansions, frames
42C40 - Wavelets and other special systems
46C50 - Generalizations of inner products (semi-inner products, partial inner products, etc.)
65T60 - Wavelets (numerical methods)
CIRM (Editeur )
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Résumé :
We start by recalling the essential features of frames, both discrete and continuous, with some emphasis on the notion of frame duality. Then we turn to generalizations, namely upper and lower semi-frames, and their duality. Next we consider arbitrary measurable maps and examine the standard operators, analysis, synthesis and frame operators, and study their properties. Finally we analyze the recent notion of reproducing pairs. In view of their duality structure, we introduce two natural partial inner product spaces and formulate a number of open questions.
Keywords: continuous frames - semi-frames - frame duality - reproducing pairs - partial inner product spaces
Codes MSC : Keywords: continuous frames - semi-frames - frame duality - reproducing pairs - partial inner product spaces
42C15 - General harmonic expansions, frames
42C40 - Wavelets and other special systems
46C50 - Generalizations of inner products (semi-inner products, partial inner products, etc.)
65T60 - Wavelets (numerical methods)
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 11/03/15 Date de captation : 23/01/15 Collection : Special events ; 30 Years of Wavelets arXiv category : Functional Analysis ; Mathematical Physics Domaine : Mathematical Physics ; Mathematics in Science & Technology ; Analysis and its Applications Format : MP4 (.mp4) - HD Durée : 00:32:08 Audience : Researchers Download : https://videos.cirm-math.fr/2015-01-23_Antoine.mp4 
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Informations sur la Rencontre
Nom de la rencontre : 30 years of wavelets / 30 ans des ondelettesOrganisateurs de la rencontre : Feichtinger, Hans G. ; Torrésani, Bruno Dates : 23/01/15 - 24/01/15 Année de la rencontre : 2015 URL Congrès : https://www.chairejeanmorlet.com/1523.html
Données de citation
DOI : 10.24350/CIRM.V.18715703Citer cette vidéo: Antoine, Jean-Pierre (2015). Continuous (semi-)frames revisited. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18715703 URI : http://dx.doi.org/10.24350/CIRM.V.18715703 |
Bibliographie
- [1] Ali, S.T., Antoine, J-P., & Gazeau, J-P. (1991). Square integrability of group representations on homogeneous spaces. I: reproducing triples and frames. Annales de l'Institut Henri Poincaré. Physique Théorique, 55(4), 829-855 - https://eudml.org/doc/76555
- [2] Ali, S.T., Antoine, J-P., & Gazeau, J-P. (1993). Continuous frames in Hilbert space. Annals of Physics, 222(1), 1-37 - http://dx.doi.org/10.1006/aphy.1993.1016
- [3] Antoine, J-P., & Balazs, P. (2011). Frames and semi-frames. Journal of Physics A: Mathematical and Theoretical, 44(20), 205201; corrigendum ibid. 44(47), 479501 - http://dx.doi.org/10.1088/1751-8113/44/20/205201
- [4] Antoine, J-P., & Balazs, P. (2012). Frames, semi-frames, and Hilbert scales. Numerical Functional Analysis and Optimization, 33(7-9), 736-769 - http://dx.doi.org/10.1080/01630563.2012.682128
- [5] Antoine, J-P., & Trapani, C. (2009). Partial Inner Product Spaces: theory and Applications. Berlin, Heidelberg: Springer. (Lecture Notes in Mathematics, 1986) - http://dx.doi.org/10.1007/978-3-642-05136-4
- [6] Speckbacher, M., & Balazs, P. (2014). The continuous non stationary Gabor transform on LCA groups with applications to representations of the affine Weyl-Heisenberg group.
