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On infinitely differentiable and Gevrey vectors for representation
Author:
A. F. M. ter Elst
Journal:
Proc. Amer. Math. Soc. 112 (1991), 795-802
MSC:
Primary 22E30; Secondary 22E45, 22E46
MathSciNet review:
1045134
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Abstract: In the present paper we give a condition in order that the set of infinitely differentiable vectors for a representation  in a Banach space be equal to the set of all infinitely differentiable vectors for the restriction of  to a subgroup. Similar results for Gevrey vectors and analytic vectors are proved for unitary representations.
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Antonius
Frederik Maria ter Elst, Gevrey spaces related to Lie algebras of
operators, Technische Universiteit Eindhoven, Eindhoven, 1989.
Dissertation, Technische Universiteit Eindhoven, Eindhoven, 1989; With a
Dutch summary. MR 1028061
(91c:22016)
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B. Folland, Introduction to partial differential equations,
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331–332. MR 0021943
(9,133b)
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Roe
W. Goodman, One-parameter groups generated by operators in an
enveloping algebra., J. Functional Analysis 6 (1970),
218–236. MR 0268330
(42 #3229)
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Roe
Goodman and Nolan
R. Wallach, Whittaker vectors and conical vectors, J. Funct.
Anal. 39 (1980), no. 2, 199–279. MR 597811
(82i:22018), http://dx.doi.org/10.1016/0022-1236(80)90013-0
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Derek
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57 (1988), no. 2, 357–395. MR 962512
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Michael
E. Taylor, Noncommutative harmonic analysis, Mathematical
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Providence, RI, 1986. MR 852988
(88a:22021)
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Albert
Wilansky, Modern methods in topological vector spaces,
McGraw-Hill International Book Co., New York, 1978. MR 518316
(81d:46001)
- [Bru]
- F. Bruhat, Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France 84 (1956), 97-205. MR 0084713 (18:907i)
- [tE]
- A.F.M. ter Elst, Gevrey spaces related to Lie algebras of operators, Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 1989. MR 1028061 (91c:22016)
- [Fol]
- G. B. Folland, Introduction to partial differential equations, Princeton University Press, Princeton, NJ, 1976. MR 0599578 (58:29031)
- [Går]
- L. Gårding, Note on continuous representations of Lie groups, Proc. Nat. Acad. Sci. 33 (1947), 331-332. MR 0021943 (9:133b)
- [Goo]
- R. Goodman, One-parameter groups generated by operators in an enveloping algebra, J. Funct. Anal. 6 (1970), 218-236. MR 0268330 (42:3229)
- [GW]
- R. Goodman and N. R. Wallach, Whittaker vectors and conical vectors, J. Funct. Anal. 39 (1980), 199-279. MR 597811 (82i:22018)
- [Nel]
- E. Nelson, Analytic vectors, Ann. of Math. 70 (1959), 572-615. MR 0107176 (21:5901)
- [Pou]
- N. S. Poulsen, On
 -vectors and intertwining bilinear forms for representations of Lie groups, J. Funct. Anal. 9 (1972), 87-120. MR 0310137 (46:9239)
- [Rob]
- D W. Robinson, Lie groups and Lipschitz spaces, Duke Math. J. 57 (1988), 357-395. MR 962512 (90k:22018)
- [Tay]
- M. E. Taylor, Noncommutative harmonic analysis, Math. Surveys and Monographs, vol. 22, Amer. Math. Soc., Providence, RI, 1986. MR 852988 (88a:22021)
- [Wil]
- A. Wilansky, Modern methods in topological vector spaces, McGraw-Hill, New York, 1978. MR 518316 (81d:46001)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1991-1045134-0
PII:
S 0002-9939(1991)1045134-0
Article copyright:
© Copyright 1991 American Mathematical Society
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