Displaying similar documents to “A remark on Whittaker functions on SL ( n , ℝ ) ”

The reciprocal of the beta function and G L ( n , ℝ ) Whittaker functions

Eric Stade (1994)

Annales de l'institut Fourier

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In this paper we derive, using the Gauss summation theorem for hypergeometric series, a simple integral expression for the reciprocal of Euler’s beta function. This expression is similar in form to several well-known integrals for the beta function itself. We then apply our new formula to the study of G L ( n , ℝ ) Whittaker functions, which are special functions that arise in the Fourier theory for automorphic forms on the general linear group. Specifically, we deduce explicit integral...

Oscillations of anharmonic Fourier series and the wave equation.

Alain Haraux, Vilmos Komornik (1985)

Revista Matemática Iberoamericana

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In this paper we have collected some partial results on the sign of u(t,x) where u is a (sufficiently regular) solution of ⎧     utt + (-1)m Δmu = 0     (t,x) ∈ R x Ω ⎨ ⎩     u|Γ = ... = Δm-1 u|Γ = 0     t ∈ R. These results rely on the study of a sign of almost periodic functions of a special...

On mean central limit theorems for stationary sequences

Jérôme Dedecker, Emmanuel Rio (2008)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper, we give estimates of the minimal 𝕃 1 distance between the distribution of the normalized partial sum and the limiting gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.

Comparison between criteria leading to the weak invariance principle

Olivier Durieu, Dalibor Volný (2008)

Annales de l'I.H.P. Probabilités et statistiques

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The aim of this paper is to compare various criteria leading to the central limit theorem and the weak invariance principle. These criteria are the martingale-coboundary decomposition developed by Gordin in (1969), the projective criterion introduced by Dedecker in (1998), which was subsequently improved by Dedecker and Rio in (2000) and the condition introduced by Maxwell and Woodroofe in (2000) later improved upon...