On Hardy and Bergman spaces on complex Ol'shanskiı semigroups

Krötz, Bernhard

doi:10.1007/s002080050211

Cited by 16 publications

(10 citation statements)

References 24 publications

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“…Let Γ(C) be the set of all unitary irreducible and C-dissipative representations of the group G [114]. B. Krötz [99] found a Plancherel formula for the representation π:…”

Section: Bergman Space Of a Complex Semi-group Weil Representation Amentioning

confidence: 99%

Covariant quantization: spectral analysis versus deformation theory

Pevzner

2008

Jpn. J. Math.

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Formal deformation or rather symbolic calculus? To which extent do these approaches complete each other in the study of symmetry-preserving quantization procedures for homogeneous spaces? The representation theory of underlying Lie groups shows that the answer is much more delicate than initially thought and that it cannot be always reduced to asymptotic expansions with respect to some Planck's constant. The main goal of this survey is to give hints regarding the aims of each approach and, on the domain where these intersect, to compare the answers they lead to.

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“…Let Γ(C) be the set of all unitary irreducible and C-dissipative representations of the group G [114]. B. Krötz [99] found a Plancherel formula for the representation π:…”

Section: Bergman Space Of a Complex Semi-group Weil Representation Amentioning

confidence: 99%

Covariant quantization: spectral analysis versus deformation theory

Pevzner

2008

Jpn. J. Math.

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“…This in turn has far reaching consequences for the determination of the spectrum of various G c -invariant Hilbert spaces of holomorphic functions, for instance, for Bergman spaces on the domains D (cf. [HiKr99c], [Kr98]).…”

Section: C-functions and Asymptotic Behaviour Of Spherical Functionsmentioning

confidence: 99%

Spherical functions on mixed symmetric spaces

2001

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“…8 . It turns out that the introduction of a suitable weight function produces Hardy spaces on which S does not necessarily act by c o n tractions.…”

Section: Weighted Hardy Spacesmentioning

confidence: 99%

On Weighted Hardy Spaces on Complex Semigroups

Neeb¹

1998

Semigroup Forum

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In this paper we study Hardy spaces H p S; on a complex open Ol'shanski semigroup S = G ExpiW ,w h e r e1 p 1 and is an absolute value on the involutive semigroup S . For 1 p 1 we p r o ve the existence of an isometric boundary value map H p S; ! L p G generalizing the corresponding result ofOl'shanski f o r p = 2 and = 1 . In the second part we use the ne structure of the space H 2 S; 1 to prove the existence of a bounded holomorphic function on S whose absolute value has a unique maximum in the boudary point 1 2 G and therefore complete the proof of the approximation property o f t h e P oisson kernel and the uniqueness of G as a Shilov boundary of S whenever W does not contain a ne lines. IntroductionLet G be a connected Lie group, g its Lie algebra, and W g an invariant o p e n convex cone whose interior consists of elements X for which Specad X iR.

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On Hardy and Bergman spaces on complex Ol'shanskiı semigroups

Cited by 16 publications

References 24 publications

Covariant quantization: spectral analysis versus deformation theory

Covariant quantization: spectral analysis versus deformation theory

Spherical functions on mixed symmetric spaces

On Weighted Hardy Spaces on Complex Semigroups

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