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On fractional powers of singular perturbations of the Laplacian. (English) Zbl 06901704

Summary: We qualify a relevant range of fractional powers of the so-called Hamiltonian of point interaction in three dimensions, namely the singular perturbation of the negative Laplacian with a contact interaction supported at the origin. In particular we provide an explicit control of the domain of such a fractional operator and of its decomposition into regular and singular parts. We also qualify the norms of the resulting singular fractional Sobolev spaces and their mutual control with the corresponding classical Sobolev norms.

MSC:

47A60 Functional calculus for linear operators
47B25 Linear symmetric and selfadjoint operators (unbounded)
47G10 Integral operators
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81Q80 Special quantum systems, such as solvable systems
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