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• W1888897989 abstract "Publisher Summary This chapter discusses the theory of differential and integral operators of arbitrary complex order. The chapter describes some applications of the theory in modern mathematical physics, connected with the Riesz potentials. The kernel of the Riesz method is the analytic continuation of the Riemann–Liouville “fractional” integral that is a natural extension of Cauchy's solution of an initial value problem. The widening of the semigroup of fractional integral operators of a specific type to an Abelian group is equivalent to the introduction of fractional differential operators. This is the starting-point of a newly developed branch of semigroup theory—that is, the “operational calculus of fractional powers.” The results are also interlinked with differential equations in Banach spaces and a few modern topics in functional analysis, for example, about certain operators in abstract Hilbert spaces. The chapter discusses the close connection between integro-differential operators of arbitrary complex order and some strong summation methods." @default.
• W1888897989 created "2016-06-24" @default.
• W1888897989 creator A5005035391 @default.
• W1888897989 date "1984-01-01" @default.
• W1888897989 modified "2023-10-15" @default.
• W1888897989 title "Integro-Differential Operators and Theory of Summation" @default.
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• W1888897989 doi "https://doi.org/10.1016/s0304-0208(08)70830-2" @default.
• W1888897989 hasPublicationYear "1984" @default.
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