# An F. and M. Riesz theorem for bounded symmetric domains

Annales de l'institut Fourier (1987)

- Volume: 37, Issue: 2, page 139-150
- ISSN: 0373-0956

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topBrummelhuis, R. G. M.. "An F. and M. Riesz theorem for bounded symmetric domains." Annales de l'institut Fourier 37.2 (1987): 139-150. <http://eudml.org/doc/74749>.

@article{Brummelhuis1987,

abstract = {We generalize the classical F. and M. Riesz theorem to metrizable compact groups whose center contains a copy of the circle group. Important examples of such groups are the isotropy groups of the bounded symmetric domains.The proof uses a criterion for absolute continuity involving $L^p$ spaces with $p< 1$: A measure $\mu $ on a compact metrisable group $K$ is absolutely continuous with respect to Haar measure $dk$ on $K$ if for some $p< 1$ a certain subspace of $L^p(K,dk)$ which is related to $\mu $ has sufficiently many continuous linear functionals to separate its points. For abelian $K$ this criterion is due to J.H. Shapiro.},

author = {Brummelhuis, R. G. M.},

journal = {Annales de l'institut Fourier},

keywords = {Riesz theorem; metrizable compact groups; bounded symmetric domains; absolute continuity; spaces},

language = {eng},

number = {2},

pages = {139-150},

publisher = {Association des Annales de l'Institut Fourier},

title = {An F. and M. Riesz theorem for bounded symmetric domains},

url = {http://eudml.org/doc/74749},

volume = {37},

year = {1987},

}

TY - JOUR

AU - Brummelhuis, R. G. M.

TI - An F. and M. Riesz theorem for bounded symmetric domains

JO - Annales de l'institut Fourier

PY - 1987

PB - Association des Annales de l'Institut Fourier

VL - 37

IS - 2

SP - 139

EP - 150

AB - We generalize the classical F. and M. Riesz theorem to metrizable compact groups whose center contains a copy of the circle group. Important examples of such groups are the isotropy groups of the bounded symmetric domains.The proof uses a criterion for absolute continuity involving $L^p$ spaces with $p< 1$: A measure $\mu $ on a compact metrisable group $K$ is absolutely continuous with respect to Haar measure $dk$ on $K$ if for some $p< 1$ a certain subspace of $L^p(K,dk)$ which is related to $\mu $ has sufficiently many continuous linear functionals to separate its points. For abelian $K$ this criterion is due to J.H. Shapiro.

LA - eng

KW - Riesz theorem; metrizable compact groups; bounded symmetric domains; absolute continuity; spaces

UR - http://eudml.org/doc/74749

ER -

## References

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