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Functions of several real variables --- Maximal functions --- Smoothness of functions --- Sobolev spaces

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"Let SpXq be the Schwartz space of compactly supported smooth functions on the p-adic points of a spherical variety X, and let CpXq be the space of Harish- Chandra Schwartz functions. Under assumptions on the spherical variety, which are satisfied when it is symmetric, we prove Paley-Wiener theorems for the two spaces, characterizing them in terms of their spectral transforms. As a corollary, we get relative analogs of the smooth and tempered Bernstein centers - rings of multipliers for SpXq and C pXq. When X " a reductive group, our theorem for CpXq specializes to the well-known theorem of Harish-Chandra, and our theorem for SpXq corresponds to a first step - enough to recover the structure of the Bernstein center - towards the well-known theorems of Bernstein [Ber] and Heiermann [Hei01]"--

Spherical harmonics. --- p-adic analysis. --- Fourier analysis. --- Harmoniques sphériques --- Analyse p-adique --- Fourier, Analyse de --- Schwartz spaces. --- Scattering (Mathematics) --- Smoothness of functions. --- Lie algebras.

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Moduli theory --- Smoothness of functions --- Variétés topologiques à 4 dimensions --- Modules, théorie des --- 517.5 --- Smooth functions --- Functions --- Theory of moduli --- Analytic spaces --- Functions of several complex variables --- Geometry, Algebraic --- Theory of functions --- Moduli theory. --- Smoothness of functions. --- 517.5 Theory of functions --- Variétés topologiques à 4 dimensions --- Modules, théorie des --- Fonctions d'une variable reelle --- Approximation

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"In this memoir, we show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation"--

Computer-assisted instruction --- Enseignement assisté par ordinateur --- Équations aux dérivées partielles --- Differential equations --- Linear operators --- Opérateurs linéaires --- Théorie asymptotique. --- Asymptotic theory. --- Fluid mechanics. --- Fluid dynamics --- Interval analysis (Mathematics) --- Inviscid flow. --- Flows (Differentiable dynamical systems) --- Differential equations, Nonlinear --- Smoothness of functions. --- Geostrophic currents --- Mathematical models. --- Numerical solutions.

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Mathematical analysis --- 517.54 --- 51 <082.1> --- Conformal mapping and geometric problems in the theory of functions of a complex variable. Analytic functions and their generalizations --- Mathematics--Series --- 517.54 Conformal mapping and geometric problems in the theory of functions of a complex variable. Analytic functions and their generalizations --- Harmonic functions. --- Green's functions. --- Inequalities (Mathematics) --- Smoothness of functions. --- Fonctions harmoniques. --- Green, Fonctions de. --- Inégalités (mathématiques) --- Fonctions de lissage. --- Green's functions --- Harmonic functions --- Smoothness of functions --- Smooth functions --- Functions --- Processes, Infinite --- Functions, Harmonic --- Laplace's equations --- Bessel functions --- Differential equations, Partial --- Fourier series --- Harmonic analysis --- Lamé's functions --- Spherical harmonics --- Toroidal harmonics --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics)