# A note on Howe's oscillator semigroup

Annales de l'institut Fourier (1989)

- Volume: 39, Issue: 3, page 663-688
- ISSN: 0373-0956

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topHilgert, Joachim. "A note on Howe's oscillator semigroup." Annales de l'institut Fourier 39.3 (1989): 663-688. <http://eudml.org/doc/74846>.

@article{Hilgert1989,

abstract = {Analytic extensions of the metaplectic representation by integral operators of Gaussian type have been calculated in the $L^2(\{\Bbb R\}^n)$ and the Bargmann-Fock realisations by Howe [How2] and Brunet-Kramer [Brunet-Kramer, Reports on Math. Phys., 17 (1980), 205-215]], respectively. In this paper we show that the resulting semigroups of operators are isomorphic and calculate the intertwining operator.},

author = {Hilgert, Joachim},

journal = {Annales de l'institut Fourier},

keywords = {analytic extensions of the metaplectic representation by integral operators of Gaussian type; Bargmann-Fock realisation; semigroups of operators; intertwining operator},

language = {eng},

number = {3},

pages = {663-688},

publisher = {Association des Annales de l'Institut Fourier},

title = {A note on Howe's oscillator semigroup},

url = {http://eudml.org/doc/74846},

volume = {39},

year = {1989},

}

TY - JOUR

AU - Hilgert, Joachim

TI - A note on Howe's oscillator semigroup

JO - Annales de l'institut Fourier

PY - 1989

PB - Association des Annales de l'Institut Fourier

VL - 39

IS - 3

SP - 663

EP - 688

AB - Analytic extensions of the metaplectic representation by integral operators of Gaussian type have been calculated in the $L^2({\Bbb R}^n)$ and the Bargmann-Fock realisations by Howe [How2] and Brunet-Kramer [Brunet-Kramer, Reports on Math. Phys., 17 (1980), 205-215]], respectively. In this paper we show that the resulting semigroups of operators are isomorphic and calculate the intertwining operator.

LA - eng

KW - analytic extensions of the metaplectic representation by integral operators of Gaussian type; Bargmann-Fock realisation; semigroups of operators; intertwining operator

UR - http://eudml.org/doc/74846

ER -

## References

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