Riesz potentials derived by one-mode interacting Fock space approach

Nobuhiro Asai. "Riesz potentials derived by one-mode interacting Fock space approach." Colloquium Mathematicae 109.1 (2007): 101-106. <http://eudml.org/doc/284326>.

@article{NobuhiroAsai2007,
abstract = {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 $γ_\{α,c_\{1,2\}\}$.},
author = {Nobuhiro Asai},
journal = {Colloquium Mathematicae},
keywords = {one-mode interacting Fock space; Jacobi-Szegő parameters; Segal-Bargmann transform; Bessel kernel measures; Riesz potentials; Hilbert space of analytic functions},
language = {eng},
number = {1},
pages = {101-106},
title = {Riesz potentials derived by one-mode interacting Fock space approach},
url = {http://eudml.org/doc/284326},
volume = {109},
year = {2007},
}

TY - JOUR
AU - Nobuhiro Asai
TI - Riesz potentials derived by one-mode interacting Fock space approach
JO - Colloquium Mathematicae
PY - 2007
VL - 109
IS - 1
SP - 101
EP - 106
AB - 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 $γ_{α,c_{1,2}}$.
LA - eng
KW - one-mode interacting Fock space; Jacobi-Szegő parameters; Segal-Bargmann transform; Bessel kernel measures; Riesz potentials; Hilbert space of analytic functions
UR - http://eudml.org/doc/284326
ER -