On the invertibility of the operator d/dt + A in certain functional spaces

• Datum: 2007
• Hauptverfasser: Gorodnii, M. F., Городній, М. Ф.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2007
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3365
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We prove that the operator $\cfrac{d}{dt} + A$ constructed on the basis of a sectorial operator $A$ with spectrum in the right half-plane of $ℂ$ is continuously invertible in the Sobolev spaces $W_p^1 (ℝ, D_{α}),\; α ≥ 0$. Here, $D_{α}$ is the domain of definition of the operator $A^{α}$ and the nor...