Riesz potentials derived by one-mode interacting Fock space approach

• Autorzy: Nobuhiro Asai
• Języki publikacji: EN

Abstrakty

EN

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 $γ_{α,c_{1,2}}$.

Kategorie tematyczne

• 60J45: Probabilistic potential theory
• 46N30: Applications in probability theory and statistics
• 33D45: Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 109
• Numer: 1
• Strony: 101-106

Daty

wydano

2007

Twórcy

autor

Nobuhiro Asai

• Department of Mathematics Education, Aichi University of Education, Kariya, 448-8542, Japan

Identyfikatory

DOI

10.4064/cm109-1-8