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arXiv · 1901.06118

Abstract Fractional Calculus for m-accretive Operators

Maksim V. Kukushkin
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Abstract

In this paper we aim to construct an abstract model of a differential operator with a fractional integro-differential operator composition in final terms, where modeling is understood as an interpretation of concrete differential operators in terms of the infinitesimal generator of a corresponding semigroup. We study such operators as a Kipriyanov operator, Riesz potential, difference operator. Along with this, we consider transforms of m-accretive operators as a generalization, introduce an operator class $\mathfrak{G_{\alpha}}$ and provide a description of its spectral properties.

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Maksim V. Kukushkin. 2019-01-18. Abstract Fractional Calculus for m-accretive Operators. https://arxiv.org/abs/1901.06118

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