Semigroups generated by certain pseudo-differential operators on the half-space ${ℝ}_{0+}^{n+1}$

Victoria Knopova. "Semigroups generated by certain pseudo-differential operators on the half-space $ℝ_{0+}^{n+1}$." Colloquium Mathematicae 101.2 (2004): 221-236. <http://eudml.org/doc/283642>.

@article{VictoriaKnopova2004,
abstract = {The aim of the paper is two-fold. First, we investigate the ψ-Bessel potential spaces on $ℝ_\{0+\}^\{n+1\}$ and study some of their properties. Secondly, we consider the fractional powers of an operator of the form $-A_± = -ψ(D_\{x^\{\prime \}\}) ± ∂/(∂x_\{n+1\})$, $(x^\{\prime \},x_\{n+1\}) ∈ ℝ^\{n+1\}_\{0+\}$, where $ψ(D_\{x^\{\prime \}\})$ is an operator with real continuous negative definite symbol ψ: ℝⁿ → ℝ. We define the domain of the operator $-(-A_±)^\{α\}$ and prove that with this domain it generates an $L_\{p\}$-sub-Markovian semigroup.},
author = {Victoria Knopova},
journal = {Colloquium Mathematicae},
keywords = {pseudo-differential operator; sub-Markovian semigroup; Bessel potentials; fractional powers of operators},
language = {eng},
number = {2},
pages = {221-236},
title = {Semigroups generated by certain pseudo-differential operators on the half-space $ℝ_\{0+\}^\{n+1\}$},
url = {http://eudml.org/doc/283642},
volume = {101},
year = {2004},
}

TY - JOUR
AU - Victoria Knopova
TI - Semigroups generated by certain pseudo-differential operators on the half-space $ℝ_{0+}^{n+1}$
JO - Colloquium Mathematicae
PY - 2004
VL - 101
IS - 2
SP - 221
EP - 236
AB - The aim of the paper is two-fold. First, we investigate the ψ-Bessel potential spaces on $ℝ_{0+}^{n+1}$ and study some of their properties. Secondly, we consider the fractional powers of an operator of the form $-A_± = -ψ(D_{x^{\prime }}) ± ∂/(∂x_{n+1})$, $(x^{\prime },x_{n+1}) ∈ ℝ^{n+1}_{0+}$, where $ψ(D_{x^{\prime }})$ is an operator with real continuous negative definite symbol ψ: ℝⁿ → ℝ. We define the domain of the operator $-(-A_±)^{α}$ and prove that with this domain it generates an $L_{p}$-sub-Markovian semigroup.
LA - eng
KW - pseudo-differential operator; sub-Markovian semigroup; Bessel potentials; fractional powers of operators
UR - http://eudml.org/doc/283642
ER -