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Riesz potentials derived by one-mode interacting Fock space approach

Nobuhiro Asai — 2007

Colloquium Mathematicae

The main aim of this short paper is to study Riesz potentials on one-mode interacting Fock spaces equipped with deformed annihilation, creation, and neutral operators with constants c 0 , 0 , c 1 , 1 and c 0 , 1 > 0 , c 1 , 2 0 as in equations (1.4)-(1.6). First, to emphasize the importance of these constants, we summarize our previous results on the Hilbert space of analytic L² functions with respect to a probability measure on ℂ. Then we consider the Riesz kernels of order 2α, α = c 0 , 1 / c 1 , 2 , on ℂ if 0 < c 0 , 1 < c 1 , 2 , which can be derived from the Bessel...

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