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Riesz potentials derived by one-mode interacting Fock space approach

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Asai N.

Colloquium Mathematicum

2007

tom 109

nr 1

101-106

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 $c_{0,0},c_{1,1} ∈ ℝ$ 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 kernels of order 2α, $γ_{α,c_{1,2}}$, on ℂ. Moreover, we prove that if $c_{1,2}/2 < c_{0,1} < c_{1,2}$, then the Riesz potentials are continuous linear operators on the Hilbert space of analytic L² functions with respect to $γ_{α,c_{1,2}}$.

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1 Colloquium Mathematicum

1 Asai N.

1 2007

Wyniki wyszukiwania

Riesz potentials derived by one-mode interacting Fock space approach