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A characterisation of dilation-analytic operators. (English) Zbl 0624.47022

The main aim of this paper is to analyse the class of dilation-analytic operators in a new representation of quantum mechanics on a space of analytic functions on the upper half-plane to a Hilbert space. A characterization of dilation-analytic operators is given in terms of certain analytic continuation properties of the integral kernel. The characterization of dilation-analytic vectors, which was first obtained by D. Babbitt and E. Balslev [J. Funct. Analysis 18, 1-14 (1975; Zbl 0304.47009)], is recovered in an easy way. A dilation analyticity criterion is given for an integral operator in momentum space.
Reviewer: Wu Jingbo

MSC:

47B38 Linear operators on function spaces (general)
47A20 Dilations, extensions, compressions of linear operators
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
45P05 Integral operators

Citations:

Zbl 0304.47009
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References:

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