Abstract
We prove that the operator 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 1p (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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1020–1025, August, 2007.
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Horodnii, M.F. On the invertibility of the operator d/dt + A in certain functional spaces. Ukr Math J 59, 1130–1136 (2007). https://doi.org/10.1007/s11253-007-0074-4
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DOI: https://doi.org/10.1007/s11253-007-0074-4