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- W10565000 abstract "Suppose I is an open real interval, and V a subspace of C∞(I) invariant under D, differentiation. It is shown that if V contains a polynomial of positive degree, then D has no homogeneous qth root on V, for any integer q > 1. This conclusion is not generally true if I is replaced by an arbitrary open set in the reals. Necessary and sufficient conditions for the existence of qth roots of D on finite dimensional subspaces of C∞(I) invariant under D, in terms of the differential equations of which such subspaces are the solution spaces, are obtained.KeywordsCharacteristic PolynomialOpen IntervalReal Vector SpaceComplex Vector SpacePositive DegreeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
- W10565000 created "2016-06-24" @default.
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- W10565000 date "1975-01-01" @default.
- W10565000 modified "2023-10-17" @default.
- W10565000 title "An algebraic definition of fractional differentiation" @default.
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- W10565000 doi "https://doi.org/10.1007/bfb0067107" @default.
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