Connection between the Plancherel formula and the Howe dual pair (Sp(2n, ℝ), O(k))

Salem Ben Saïd

doi:10.1007/s00209-002-0443-5

Connection between the Plancherel formula and the Howe dual pair (Sp(2n, ℝ), O(k))

Salem Ben Saïd

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Let D be the bounded symmetric domain {w ∈ Sym(2n, ℂ)| I_2n - ww̄ ≫ 0}. In this article, we describe explicitly the Plancherel formula of a weighted Bergman space on D under the action of Sp_c(2n, ℝ) × Sp_c(2n, ℝ) by using the Howe dual pair (Sp_c(2n, ℝ), O(k)).

Original language	English
Pages (from-to)	743-760
Number of pages	18
Journal	Mathematische Zeitschrift
Volume	241
Issue number	4
DOIs	https://doi.org/10.1007/s00209-002-0443-5
Publication status	Published - Dec 2002
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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title = "Connection between the Plancherel formula and the Howe dual pair (Sp(2n, ℝ), O(k))",

abstract = "Let D be the bounded symmetric domain {w ∈ Sym(2n, ℂ)| I2n - w{\=w} ≫ 0}. In this article, we describe explicitly the Plancherel formula of a weighted Bergman space on D under the action of Spc(2n, ℝ) × Spc(2n, ℝ) by using the Howe dual pair (Spc(2n, ℝ), O(k)).",

author = "{Ben Sa{\"i}d}, Salem",

year = "2002",

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doi = "10.1007/s00209-002-0443-5",

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N2 - Let D be the bounded symmetric domain {w ∈ Sym(2n, ℂ)| I2n - ww̄ ≫ 0}. In this article, we describe explicitly the Plancherel formula of a weighted Bergman space on D under the action of Spc(2n, ℝ) × Spc(2n, ℝ) by using the Howe dual pair (Spc(2n, ℝ), O(k)).

AB - Let D be the bounded symmetric domain {w ∈ Sym(2n, ℂ)| I2n - ww̄ ≫ 0}. In this article, we describe explicitly the Plancherel formula of a weighted Bergman space on D under the action of Spc(2n, ℝ) × Spc(2n, ℝ) by using the Howe dual pair (Spc(2n, ℝ), O(k)).

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Connection between the Plancherel formula and the Howe dual pair (Sp(2n, ℝ), O(k))

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