2017
Том 69
№ 9

All Issues

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

Gorodnii M. F.

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Abstract

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 norm in $D_{α}$ is the norm of the graph of $A^{α}$.

English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 8, pp 1130-1136.

Citation Example: Gorodnii M. F. On the invertibility of the operator d/dt + A in certain functional spaces // Ukr. Mat. Zh. - 2007. - 59, № 8. - pp. 1020–1025.

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