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Toeplitz and Hankel operators on Bargmann spaces

Published online by Cambridge University Press:  18 May 2009

Jan Janas
Jan Janas
Affiliation:
Instytut Matematyczny, PAN, 31-027 Krakow, Ul. Solskiego 30, Polska.
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Let μ be the Gaussian measure in ℂn given by dμ(z)=(2π)−n exp(−|z|2/2)dV, where dV is the ordinary Lebesgue measure in ℂn. The Segal-Bargmann space H2(μ) is the space of all entire functions on ℂn that belong to L2(μ)-the usual space of Gaussian square-integrable functions. Let P be the orthogonal projection from L2(μ) onto H2(μ). For a measurable function ϕ on ℂn, the multiplication operator Mϕ on L2(μ) is defined by Mϕh =ϕh. The Toeplitz operator Tϕ is defined on H2(μ)by

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 3 , September 1988 , pp. 315 - 323
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

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