Laboratoire de Mathématiques de Besançon - UMR 6623 CNRS

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3 avril 2018: 1 événement

  • Séminaire d’Analyse Fonctionnelle

    Mardi 3 avril 13:45-15:00 - Rauan Akylzhanov - Imperial College London

    Smooth dense subalgebras and Fourier multipliers on compact quantum groups

    Résumé : We define and study dense Frechet subalgebras of compact quantum groups consisting of elements rapidly decreasing with respect to an unbounded self-adjoint Dirac-like operator with compact resolvent. Further, we characterise the boundedness of its commutators in terms of the eigenvalues. Grotendieck’s theory of topological tensor products immediately yields a Schwartz kernel theorem for linear operators on compact quantum groups and allows us to introduce a natural class of pseudo-differential operators on compact quantum groups. Further, we show that composition of two regular pseudo-differential operators is a regular pseudo-differential operator. As a by-product, we develop elements of the distribution theory and corresponding Fourier analysis. We give applications of our construction to obtain sufficient conditions for Lp - Lq boundedness of coinvariant linear operators. We provide necessary and sufficient conditions for algebraic differential calculi on Hopf subalgebras of compact quantum groups to extend to the proposed smooth structure. We check explicitly that these conditions hold true on the quantum SUq(2) for both its 3-dimensional and 4-dimensional calculi.
    Joint work with Michael Ruzhansky and Shahn Majid.

    En savoir plus : Séminaire d’Analyse Fonctionnelle