Lie Semigroups and their Applications

Hilgert, Joachim; Neeb, Karl-Hermann

doi:10.1007/bfb0084640

Cited by 107 publications

(154 citation statements)

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“…In this appendix we prove an important generalization of a result of Ol shanskiȋ ([HiNe93,Prop. 9.18], cf.…”

Section: Appendix B: the Holomorphic Extension Theoremmentioning

confidence: 83%

“…[Wa72, p.296]). The following theorem is a substantially improved version of Theorem 9.39 in [HiNe93] (cf. also [LM75]) which no longer needs the assumption that the representation under consideration is a representation by contractions and that it extends to a continuous representation of the closed cone.…”

Section: The Lüscher-mack Correspondencementioning

confidence: 99%

“…With this information at hand we can now use the arguments given in steps 3 through 5 in the proof of [HiNe93,Thm. 9.39] to complete the proof of Theorem 3.1.…”

Section: The Lüscher-mack Correspondencementioning

confidence: 99%

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Positive definite spherical functions on Olshanskii domains

Hilgert

Neeb

1999

Trans. Amer. Math. Soc.

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Abstract. Let G be a simply connected complex Lie group with Lie algebra g, h a real form of g, and H the analytic subgroup of G corresponding to h. The symmetric space M = H\G together with a G-invariant partial order ≤ is referred to as an Ol shanskiȋ space. In a previous paper we constructed a family of integral spherical functions φµ on the positive domain M + := {Hx : Hx ≥ H} of M. In this paper we determine all of those spherical functions on M + which are positive definite in a certain sense.

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“…In this appendix we prove an important generalization of a result of Ol shanskiȋ ([HiNe93,Prop. 9.18], cf.…”

Section: Appendix B: the Holomorphic Extension Theoremmentioning

confidence: 83%

Section: The Lüscher-mack Correspondencementioning

confidence: 99%

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Positive definite spherical functions on Olshanskii domains

Hilgert

Neeb

1999

Trans. Amer. Math. Soc.

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“…Then (cf. [8]) F = Gexp(C) is a closed semigroup contained in GL(2,C). The decomposition F = Gexp( (7) is the so-called OUshanskiz decomposition.…”

Section: X^jx-j =(-; ;)mentioning

confidence: 99%

Function spaces on the Olśhanskiĭsemigroup and the Gel'fand-Gindikin program

Koufany¹,

Ørsted²

1996

Annales De L’institut Fourier

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“…This was proved in [St86] using a result of Rothschild ( [PR72]) which says that two Cartan subalgebras in ᒄ are conjugate under G ‫ރ‬ if and only if they are conjugate under G. In [HN93] and [La94] this double coset decomposition was a main tool for examining maximal subsemigroups of G ‫ރ‬ that contain G nonisolated.…”

Section: Introductionmentioning

confidence: 99%