Toeplitz and Hankel operators on Bargmann spaces

Janas, Jan

Glasgow mathematical journal, Tome 30 (1988) no. 3, pp. 315-323

Résumé

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

Détail

DOI : 10.1017/S0017089500007400

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