2001/04/27 by Nobuhiro Asai, Asai, Nobuhiro
Mathematics · #33D45 #44A20 #81R30 #81S25 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Representation Theory (math.RT) #math.CA #math.RT #msc:33D45 #msc:44A20 #msc:81R30 #msc:81S25
paper · pdf · doi:10.48550/arxiv.math/0104260
Accepted for the publication in "Quantum Information IV", T. Hida and K. Saito (eds.), World Scientific. Minor misprints have been fixed. Reference information has been updated
openalex publication_date 2001/04/27 · arxiv created 2001/11/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let μp(q) be the q-deformed Poisson measure in the sense of Saitoh Yoshida and νp be the measure given by Equation \eqrefeq:nu-q. In this short paper, we introduce the q-deformed analogue of the Segal-Bargmann transform associated with μp(q). We prove that our Segal-Bargmann transform is a unitary map of L2(μp(q)) onto the q-deformed Hardy space \cal H2(νq). Moreover, we give the Segal-Bargmann representation of the multiplication operator by x in L2(μp(q)), which is a linear combination of the q-creation, q-annihilation, q-number, and scalar operators.