Subcritical approximation of the Sobolev quotient and a related concentration result
Giampiero Palatucci (2011)
Rendiconti del Seminario Matematico della Università di Padova
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Giampiero Palatucci (2011)
Rendiconti del Seminario Matematico della Università di Padova
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Jean-Pierre Gazeau, Jean-Louis Verger-Gaugry (2004)
Journal de Théorie des Nombres de Bordeaux
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We investigate in a geometrical way the point sets of obtained by the -numeration that are the -integers where is a Perron number. We show that there exist two canonical cut-and-project schemes associated with the -numeration, allowing to lift up the -integers to some points of the lattice ( degree of ) lying about the dominant eigenspace of the companion matrix of . When is in particular a Pisot number, this framework gives another proof of the fact...
M. Grigorian (1999)
Studia Mathematica
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It is proved that if is a complete orthonormal system of bounded functions and ɛ>0, then there exists a measurable set E ⊂ [0,1] with measure |E|>1-ɛ, a measurable function μ(x), 0 < μ(x) ≤ 1, μ(x) ≡ 1 on E, and a series of the form , where for all q>2, with the following properties: 1. For any p ∈ [1,2) and there are numbers , k=1,2,…, = 1 or 0, such that 2. For every p ∈ [1,2) and there are a function with g(x) = f(x) on E and numbers , k=1,2,…, or 0,...
Ferenc Móricz (1994)
Studia Mathematica
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be a double sequence of real numbers which is summable (C,1,1) to a finite limit. We give necessary and sufficient conditions under which converges in Pringsheim’s sense. These conditions are satisfied if is slowly decreasing in certain senses defined in this paper. Among other things we deduce the following Tauberian theorem of Landau and Hardy type: If is summable (C,1,1) to a finite limit and there exist constants and H such that , and whenever , then...
Spira, Robert (1970)
Portugaliae mathematica
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Jean-Loup Mauclaire (2000)
Journal de théorie des nombres de Bordeaux
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Let , be a Cantor scale, the compact projective limit group of the groups , identified to , and let be its normalized Haar measure. To an element , of we associate the sequence of integral valued random variables . The main result of this article is that, given a complex -multiplicative function of modulus , we have
Jacek Pomykała (1997)
Journal de théorie des nombres de Bordeaux
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Let be a modular elliptic curve over denote the -th derivative of its Hasse-Weil -series. We estimate the number of twisted elliptic curves such that .
C. Rajagopal (1961)
Annales Polonici Mathematici
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Frank Mantlik (1991)
Annales de l'institut Fourier
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Let be a differential operator with constant coefficients depending analytically on a parameter . Assume that the family P(,D) is of constant strength. We investigate the equation where is a given analytic function of with values in some space of distributions and the solution is required to depend analytically on , too. As a special case we obtain a regular fundamental solution of P(,D) which depends analytically on . This result answers a question of L. Hörmander. ...