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Multi angle Continuous (semi-)frames revisited

Auteurs : Antoine, Jean-Pierre (Auteur de la Conférence)
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 :
    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)

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 11/03/15
      Date de captation : 23/01/15
      Collection : Special events ; 30 Years of Wavelets
      Format : quicktime ; audio/x-aac
      Durée : 00:32:08
      Domaine : Mathematical Physics ; Mathematics in Science & Technology ; Analyse & Applications
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : http://videos.cirm-math.fr/2015-01-23_Antoine.mp4

    Informations sur la rencontre

    Nom du congrès : 30 years of wavelets / 30 ans des ondelettes
    Organisteurs Congrès : Feichtinger, Hans G. ; Torrésani, Bruno
    Dates : 23/01/15 - 24/01/15
    Année de la rencontre : 2015
    URL Congrès : http://feichtingertorresani.weebly.com/3...

    Citation Data

    DOI : 10.24350/CIRM.V.18715703
    Cite 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


    Bibliographie

    1. [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. [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. [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. [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. [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. [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. <arXiv:1404.6830> - http://arxiv.org/abs/1407.6830v1

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