The Topology of the Spectrum for Gelfand Pairs on Lie Groups

Fabio Ferrari Ruffino

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 569-579
  • ISSN: 0392-4041

Abstract

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Given a Gelfand pair of Lie groups, we identify the spectrum with a suitable subset of ℂ n and we prove the equivalence between Gelfand topology and euclidean topology.

How to cite

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Ferrari Ruffino, Fabio. "The Topology of the Spectrum for Gelfand Pairs on Lie Groups." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 569-579. <http://eudml.org/doc/290444>.

@article{FerrariRuffino2007,
abstract = {Given a Gelfand pair of Lie groups, we identify the spectrum with a suitable subset of $\mathbb\{C\}^n$ and we prove the equivalence between Gelfand topology and euclidean topology.},
author = {Ferrari Ruffino, Fabio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {569-579},
publisher = {Unione Matematica Italiana},
title = {The Topology of the Spectrum for Gelfand Pairs on Lie Groups},
url = {http://eudml.org/doc/290444},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Ferrari Ruffino, Fabio
TI - The Topology of the Spectrum for Gelfand Pairs on Lie Groups
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 569
EP - 579
AB - Given a Gelfand pair of Lie groups, we identify the spectrum with a suitable subset of $\mathbb{C}^n$ and we prove the equivalence between Gelfand topology and euclidean topology.
LA - eng
UR - http://eudml.org/doc/290444
ER -

References

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  2. CHECCUCCI, V. - TOGNOLI, A. - VESENTINI, E., Lezioni di topologia generale, FeltrinelliMilano, 1977. 
  3. DUGUNDJI, J., Topology, Boston: Allyn and Bacon Inc., 1966. MR193606
  4. FARAUT, J., Analyse harmonique sur es paires de Guelfand et les espaces hyperboliques, in Analyse Harmonique, C.I.M.P.A., 1982. MR748870
  5. GILBARG, D. - TRUDINGER, N. S., Elliptic partial differential equations of second order, Springer-Verlag, 1983. Zbl0562.35001MR737190DOI10.1007/978-3-642-61798-0
  6. HELGASON, S., Differential geometry and symmetric spaces, Academic Press, 1962. Zbl0111.18101MR145455
  7. HELGASON, S., Groups and geometric analysis, Academic Press, 1984. Zbl0543.58001MR754767
  8. RUDIN, W., Fourier analysis on groups, Interscience publishers, 1977. MR152834
  9. RUDIN, W., Real and complex analysis, McGraw-Hill, 1987. Zbl0925.00005MR924157

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