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• W986594838 abstract "This article reviews several definitions of the fractional Laplace operator (-Delta)^{alpha/2} (0 < alpha < 2) in R^d, also known as the Riesz fractional derivative operator, as an operator on Lebesgue spaces L^p, on the space C_0 of continuous functions vanishing at infinity and on the space C_{bu} of bounded uniformly continuous functions. Among these definitions are ones involving singular integrals, semigroups of operators, Bochner's subordination and harmonic extensions. We collect and extend known results in order to prove that all these definitions agree: on each of the function spaces considered, the corresponding operators have common domain and they coincide on that common domain." @default.
• W986594838 created "2016-06-24" @default.
• W986594838 creator A5005079203 @default.
• W986594838 date "2017-02-01" @default.
• W986594838 modified "2023-10-11" @default.
• W986594838 title "Ten Equivalent Definitions of the Fractional Laplace Operator" @default.
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• W986594838 doi "https://doi.org/10.1515/fca-2017-0002" @default.
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