# Smooth operators for the regular representation on homogeneous spaces

Studia Mathematica (2000)

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

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topMelo, 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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