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Continuous (semi-)frames revisited
Multi angle
Authors : Antoine, Jean-Pierre (Author of the conference)
CIRM (Publisher )
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 (Publisher )
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Abstract :
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
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 11/03/15 Conference Date : 23/01/15 Series : Special events ; 30 Years of Wavelets arXiv category : Functional Analysis ; Mathematical Physics Mathematical Area(s) : Mathematical Physics ; Mathematics in Science & Technology ; Analysis and its Applications Format : MP4 (.mp4) - HD Video Time : 00:32:08 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-01-23_Antoine.mp4 
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Information on the Event
Event Title : 30 years of wavelets / 30 ans des ondelettesEvent Organizers : Feichtinger, Hans G. ; Torrésani, Bruno Dates : 23/01/15 - 24/01/15 Event Year : 2015 Event URL : https://www.chairejeanmorlet.com/1523.html
Citation Data
DOI : 10.24350/CIRM.V.18715703Cite this video as: 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 |
Bibliography
- [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.
