Abstract
Given two -sectorial operators in a reflexive Banach space , a sufficient condition is presented for the family to be holomorphic of type (A), where is a closed convex region in the -plane such that is the left branch of a hyperbola. The abstract formulation is almost identical with Kato’s when is a Hilbert space. However, is typically reduced to a parabola when is a Hilbert space. The -sectoriality is a generalized notion of the nonnegative selfadjointness so that Schrödinger operators with singular potentials in the -spaces are typical examples of the abstract theory. In this connection a detailed analysis is given in the case of . This application is an -generalization of Kato’s.
Acknowledgments
The authors want to thank the referee for reading their manuscript carefully. Especially a lot of comments are helpful to make it as readable as possible.
Citation
Yoshiki Maeda. Noboru Okazawa*. "Holomorphic families of Schrödinger operators in ." SUT J. Math. 47 (2) 185 - 216, June 2011. https://doi.org/10.55937/sut/1328712856
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