Théorie Élémentaire des Fonctions Analytiques d'une ou Plusieurs Variables Complexes

SERBIULA (sistema Librum 2.0) 01/1961;
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5a. ed. es una reimpresión de la 4a. ed

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    • "Onthehalf-linesξ≥π/Landξ≤−π/Lweproceedinadifferentway.Bya formulaincomplexanalysis(seeforinstanceChap.V,§4in[4] "
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    ABSTRACT: We prove bounds for twisted ergodic averages for horocycle flows of hyperbolic surfaces, both in the compact and in the non-compact finite area case. From these bounds we derive effective equidistribution results for horocycle maps. As an application of our main theorems in the compact case we further improve on a result of A. Venkatesh, recently already improved by J. Tanis and P. Vishe, on a sparse equidistribution problem for classical horocycle flows proposed by N. Shah and G. Margulis, and in the general non-compact, finite area case we prove bounds on Fourier coefficients of cups forms which are off the best known bounds of A. Good only by a logarithmic term. Our approach is based on Sobolev estimates for solutions of the cohomological equation and on scaling of invariant distributions for twisted horocycle flows.
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    • "Note that assumption P1 implies that m(·, ξ ) admits an holomorphic extension to the whole right half-plane. Indeed, it follows from Schwarz' reflection principle ([8] "
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    ABSTRACT: We present a new approach to study the symmetry of minimizers for a large class of nonlocal variational problems. This approach which generalizes the Reflection method is based on the existence of some integral identities. We study the identities that lead to symmetry results, the functionals that can be considered and the function spaces that can be used. Then we use our method to prove the symmetry of minimizers for a class of variational problems involving the fractional powers of Laplacian, for the generalized Choquard functional and for the standing waves of the Davey–Stewartson equation.
    Journal of Functional Analysis 01/2008; 254(2-254):535-592. DOI:10.1016/j.jfa.2007.10.004 · 1.32 Impact Factor
  • Journal of the London Mathematical Society 04/1972; DOI:10.1112/jlms/s2-4.3.418 · 0.82 Impact Factor
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