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

• Autorzy: Victoria Knopova
• Języki publikacji: EN

Abstrakty

EN

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
$-A_± = -ψ(D_{x'}) ± ∂/(∂x_{n+1})$, $(x',x_{n+1}) ∈ ℝ^{n+1}_{0+}$,
where $ψ(D_{x'})$ 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.

Kategorie tematyczne

• 60J35: Transition functions, generators and resolvents
• 46B70: Interpolation between normed linear spaces
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 60J75: Jump processes

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2004
• Tom: 101
• Numer: 2
• Strony: 221-236

Daty

wydano

2004

Twórcy

autor

Victoria Knopova

• V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, 40, Acad. V. M. Glushkov Ave., 03187 Kiev, Ukraine

Identyfikatory

DOI

10.4064/cm101-2-6