Displaying similar documents to “The weak Paley-Wiener property for group extensions.”

Invariant measure for some differential operators and unitarizing measure for the representation of a Lie group. Examples in finite dimension

Hélène Airault, Habib Ouerdiane (2011)

Banach Center Publications

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Consider a Lie group with a unitary representation into a space of holomorphic functions defined on a domain 𝓓 of ℂ and in L²(μ), the measure μ being the unitarizing measure of the representation. On finite-dimensional examples, we show that this unitarizing measure is also the invariant measure for some differential operators on 𝓓. We calculate these operators and we develop the concepts of unitarizing measure and invariant measure for an OU operator (differential operator...