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Harmonic analysis

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Harmonic analysis --- Fourier, Analyse de --- Analyse harmonique

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Harmonic analysis. Fourier analysis --- Harmonic analysis --- 51 --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- 51 Mathematics --- Congresses --- Harmonic analysis - Congresses.

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Group theory --- Analytical spaces --- Linear topological spaces. --- Locally compact groups. --- Harmonic analysis --- 51 --- Mathematics --- 51 Mathematics --- Linear topological spaces --- Locally compact groups --- Topological linear spaces --- Topological vector spaces --- Vector topology --- Topology --- Vector spaces --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Compact groups --- Topological groups --- Harmonic analysis.

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These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree. The unitary irreducible representations are classified in three types: a continuous series of spherical representations; two special representations; and a countable series of cuspidal representations as defined by G.I. Ol'shiankii. Several notable subgroups of the full automorphism group are also considered. The theory of spherical functions as eigenvalues of a Laplace (or Hecke) operator on the tree is used to introduce spherical representations and their restrictions to discrete subgroups. This will be an excellent companion for all researchers into harmonic analysis or representation theory.

Trees (Graph theory) --- Graph theory --- Automorphisms. --- Harmonic analysis. --- Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Symmetry (Mathematics) --- Automorphisms --- Harmonic analysis --- Representations of groups --- Arbres (Théorie des graphes) --- Analyse harmonique --- Représentations de groupes