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Poisson-Hermite Representation of Solutions for the Equation \(\frac{{{\partial ^2}}}{{\partial {t^2}}}u\left( {x,t} \right) + {\Delta _x}u\left( {x,t} \right) - 2x\cdot{\nabla _x}u\left( {x,t} \right) = 0\)

  • Liliana Forzani
  • Wilfredo Urbina
Conference paper

Abstract

In this article we will give a characterization of solutions for the equation\( \frac{{{\partial ^2}}}{{\partial {t^2}}}u + {\Delta _z}u - 2x\cdot{\nabla _x}u = 0 \)which are Poisson-Hermite integral of L p n )-functions, \( 1 \leqslant p \leqslant \infty \), following the classical case of characterization of harmonic functions as Poisson integrals of L p -functions.

Keywords

Gaussian measure Fourier analysis Fourier analysis in several variables maximal functions Poisson-Hermite integrals Hermite expansions 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Liliana Forzani
    • 1
  • Wilfredo Urbina
    • 2
  1. 1.Departamento de MatemáticasUniversidad Nacional del Litoral and CONICETArgentina
  2. 2.Escuela de MatemáticasFacultad de Ciencias UCVCaracasVenezuela

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