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On Spectral Synthesis and Ergodicity in Spaces of Vector-Valued Functions

Published online by Cambridge University Press:  20 November 2018

Yitzhak Weit
Yitzhak Weit*
Affiliation:
University of Hawaii, Honolulu, Hawaii 96822
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Abstract

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Spectral synthesis in L∞(ℝ, ℂN), N < 1, is considered. It is is proved that sets of spectral synthesis are necessarily sets of spectral resolution.

These results are applied to investigate ergodic and mixing properties of some positive contractions on L1(G, ℂN).

Keywords

43A4560J15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 4 , 01 December 1984 , pp. 430 - 435
Copyright
Copyright © Canadian Mathematical Society 1984

Footnotes

(1)

This work has been done during a visit of the author at the University of Toronto and is partially supported by NSERC Grant A3974.

References

1. Braun, A. and Weit, Y., On invariant subspaces of continuous vector-valued functions, J. d'analyse Math. 41 (1982), 259-271.CrossRefGoogle Scholar
2. Choquet, G. and Deny, J., Sur Vequation de convolution μ = μ * σ, C.R. Acad. Sci. 250 (1960), 799-801.Google Scholar
3. Derriennic, Y., Lois “zero ou deux” pour les processur de Markov, Ann. Inst. H. Poincaré, sec. B, 12 (1976), 111-129.Google Scholar
4. Derriennic, Y. and Lin, M., Convergence des puissances de convolution sur un groupe Abélien, Preprint.Google Scholar
5. Foguel, S., On iterates of convolutions, Proc. Amer. Math. Soc. 47 (1975), 368-370.CrossRefGoogle Scholar
6. Katznelson, Y., An introduction to harmonie analysis, Wiley, John, New York, 1968.Google Scholar
7. Malliavin, P., Ensembles de résolution spectrale, Proc. Int. Congress Mathematicians (1962), 368-378.Google Scholar
8. Rosenblatt, J., Ergodic and mixing random walks on locally compact groups, Math. Annalen 257 (1981), 31-42.CrossRefGoogle Scholar
9. Weit, Y., Spectral analysis in spaces of vector-valued functions, Pacific J. Math. 91 (1980), 243-248.CrossRefGoogle Scholar