We relate non integer powers Ls, s>0 of a given (unbounded) positive self-adjoint operator L in a real separable Hilbert space H with a certain differential operator of order 2⌈s⌉, acting on even curves R→H. This extends the results by Caffarelli–Silvestre and Stinga–Torrea regarding the characterization of fractional powers of differential operators via an extension problem.
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Musina et al. (2024) studied this question.
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