Measures connected with Bargmann's representation of the q-commutation relation for q > 1

Volume 43 / 1998

Ilona Królak Banach Center Publications 43 (1998), 253-257 DOI: 10.4064/-43-1-253-257

Abstract

Classical Bargmann's representation is given by operators acting on the space of holomorphic functions with scalar product $〈z^n,z^k〉_q = δ_{n,k}[n]_q! = F(z^n \bar{z}^k)$. We consider the problem of representing the functional F as a measure. We prove the existence of such a measure for q > 1 and investigate some of its properties like uniqueness and radiality.

Authors

  • Ilona Królak

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