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August 1, 2012
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August 1, 2012
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Abstract. We prove that the Hasse–Weil L -function associated to an elliptic curve E over is of growth order one and belongs to the Selberg class with degree two. Moreover, we show that has an infinite product representation associated with the conductor .
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August 1, 2012
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Abstract. In this paper, we have proved a main theorem dealing with generalized absolute Cesàro summability factors. This theorem also includes some well-known results.
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August 1, 2012
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Abstract. We formulate in this note some analogues of certain classical uncertainty principles in the setting of some solvable Lie groups. Some sharpness problems are also treated. The orbit method and the Plancherel theory turn out to be an important ingredient to prove such analogues. Some other Lie groups cases are also discussed.
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Abstract. In this paper, we obtain existence result for prescribed curvature satisfying a CR “flatness condition” by using topological methods results: the theory of critical points at infinity.
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August 1, 2012
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Abstract. Let G be a locally compact group and K be a compact group of automorphisms of G . We consider the functional equation where is a continuous function, is a weakly continuous function and (,) is a Hilbert space. This equation is a generalization of Gajda's functional equation of d'Alembert type. If is a solution of this equation, then the functions f and a are K -invariant and f is K -positive definite, i.e. the kernel is positive definite. This kernel is the reproducing kernel of a Hilbert space of functions on G , and this implies several properties for f . If is of finite dimensional, we show that the general solution of this equation is of the form where is an operator valued K -spherical function, with ( is the adjoint operator of ) and . As an application Chojnacki's and Stetkær's results on operator-valued spherical functions are used to give explicit solution formulas of this equation, in terms of strongly continuous unitary representations of G .
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August 1, 2012
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Abstract. The object of the present article is to investigate the Schwarz and Dirichlet boundary value problems for the inhomogeneous Cauchy–Riemann equation in an infinite sector. Firstly, we obtain the Schwarz–Poisson formula in a sector with angle (). Secondly, boundary behaviors of some linear integrals will be studied, especially at the corner point. Finally, the solutions and the conditions of solvability are explicitly obtained.
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August 1, 2012
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Abstract. In this paper, we study joint dilation scaling sets, MSF multiwavelets and non-MSF multiwavelets for reducing subspaces of . We characterize scaling sets having three-intervals by dilations 2 and , and discuss joint dilation wavelet sets obtained from these joint dilation scaling sets and also from generalized Journé wavelet sets. Further, we provide a method to obtain joint dilation scaling sets in higher dimensions through scaling sets of lower dimensions and hence obtain multiwavelet sets by dilations A and B .