-adic analytic interpolation
Jesus Araujo, Alain Escassut (1995)
Annales mathématiques Blaise Pascal
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Jesus Araujo, Alain Escassut (1995)
Annales mathématiques Blaise Pascal
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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. ...
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,...
Paolo Codecà, Roberto Dvornicich, Umberto Zannier (1998)
Journal de théorie des nombres de Bordeaux
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We study two rather different problems, one arising from Diophantine geometry and one arising from Fourier analysis, which lead to very similar questions, namely to the study of the ranks of matrices with entries either zero or , where denotes the “centered” fractional part of . These ranks, in turn, are closely connected with the non-vanishing of the Dirichlet -functions at .
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...
Lars Hörmander (2004)
Annales de l’institut Fourier
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Let be a complex analytic manifold of dimension with a hermitian metric and boundary, and let be the self-adjoint -Neumann operator on the space of forms of type . If the Levi form of has everywhere at least positive or at least negative eigenvalues, it is well known that has finite dimension and that the range of is the orthogonal complement. In this paper it is proved that dim if the range of is closed and the Levi form of...
T. Godoy, L. Saal, M. Urciuolo (1997)
Colloquium Mathematicae
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Let m: ℝ → ℝ be a function of bounded variation. We prove the -boundedness, 1 < p < ∞, of the one-dimensional integral operator defined by where for a family of functions satisfying conditions (1.1)-(1.3) given below.