A.e. convergence of anisotropic partial Fourier integrals on
Euclidean spaces and Heisenberg groups
Colloquium Mathematicum, Tome 118 (2010) no. 1, pp. 333-347
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We define partial spectral integrals $S_R$ on the Heisenberg
group by means of localizations to isotropic or anisotropic dilates
of suitable star-shaped subsets $V$ containing the joint spectrum of
the partial sub-Laplacians and the central derivative. Under the
assumption that an $L^2$-function $f$ lies in the logarithmic
Sobolev space given by $\log(2+L_\alpha)f\in L^2,$ where $L_\alpha$ is a
suitable “generalized” sub-Laplacian associated to the dilation
structure, we show that $S_Rf(x)$ converges a.e. to $f(x)$ as
$R\to\infty.$
Keywords:
define partial spectral integrals heisenberg group means localizations isotropic anisotropic dilates suitable star shaped subsets containing joint spectrum partial sub laplacians central derivative under assumption function lies logarithmic sobolev space given log alpha where alpha suitable generalized sub laplacian associated dilation structure converges infty
Affiliations des auteurs :
D. Müller 1 ; E. Prestini 2
@article{10_4064_cm118_1_18,
author = {D. M\"uller and E. Prestini},
title = {A.e. convergence of anisotropic partial {Fourier} integrals {on
Euclidean} spaces and {Heisenberg} groups},
journal = {Colloquium Mathematicum},
pages = {333--347},
publisher = {mathdoc},
volume = {118},
number = {1},
year = {2010},
doi = {10.4064/cm118-1-18},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm118-1-18/}
}
TY - JOUR AU - D. Müller AU - E. Prestini TI - A.e. convergence of anisotropic partial Fourier integrals on Euclidean spaces and Heisenberg groups JO - Colloquium Mathematicum PY - 2010 SP - 333 EP - 347 VL - 118 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/cm118-1-18/ DO - 10.4064/cm118-1-18 LA - en ID - 10_4064_cm118_1_18 ER -
%0 Journal Article %A D. Müller %A E. Prestini %T A.e. convergence of anisotropic partial Fourier integrals on Euclidean spaces and Heisenberg groups %J Colloquium Mathematicum %D 2010 %P 333-347 %V 118 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/cm118-1-18/ %R 10.4064/cm118-1-18 %G en %F 10_4064_cm118_1_18
D. Müller; E. Prestini. A.e. convergence of anisotropic partial Fourier integrals on Euclidean spaces and Heisenberg groups. Colloquium Mathematicum, Tome 118 (2010) no. 1, pp. 333-347. doi: 10.4064/cm118-1-18
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