Smooth operators for the regular representation on homogeneous spaces

Severino Melo

Studia Mathematica (2000)

  • Volume: 142, Issue: 2, page 149-157
  • ISSN: 0039-3223

Abstract

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A necessary and sufficient condition for a bounded operator on , M a Riemannian compact homogeneous space, to be smooth under conjugation by the regular representation is given. It is shown that, if all formal ’Fourier multipliers with variable coefficients’ are bounded, then they are also smooth. In particular, they are smooth if M is a rank-one symmetric space.

How to cite

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Melo, Severino. "Smooth operators for the regular representation on homogeneous spaces." Studia Mathematica 142.2 (2000): 149-157. <http://eudml.org/doc/216794>.

@article{Melo2000,
abstract = {A necessary and sufficient condition for a bounded operator on $L^2(M)$, M a Riemannian compact homogeneous space, to be smooth under conjugation by the regular representation is given. It is shown that, if all formal ’Fourier multipliers with variable coefficients’ are bounded, then they are also smooth. In particular, they are smooth if M is a rank-one symmetric space.},
author = {Melo, Severino},
journal = {Studia Mathematica},
keywords = {Riemannian manifold; Fourier multipliers; Fourier multipliers with variable coefficients; signature; Riemannian compact homogeneous space; regular representation},
language = {eng},
number = {2},
pages = {149-157},
title = {Smooth operators for the regular representation on homogeneous spaces},
url = {http://eudml.org/doc/216794},
volume = {142},
year = {2000},
}

TY - JOUR
AU - Melo, Severino
TI - Smooth operators for the regular representation on homogeneous spaces
JO - Studia Mathematica
PY - 2000
VL - 142
IS - 2
SP - 149
EP - 157
AB - A necessary and sufficient condition for a bounded operator on $L^2(M)$, M a Riemannian compact homogeneous space, to be smooth under conjugation by the regular representation is given. It is shown that, if all formal ’Fourier multipliers with variable coefficients’ are bounded, then they are also smooth. In particular, they are smooth if M is a rank-one symmetric space.
LA - eng
KW - Riemannian manifold; Fourier multipliers; Fourier multipliers with variable coefficients; signature; Riemannian compact homogeneous space; regular representation
UR - http://eudml.org/doc/216794
ER -

References

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