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Fractional powers of the algebraic sum of normal operators. (English) Zbl 1092.47027
The author establishes sufficient conditions governing the following fact: if \(A\) and \(B\) are unbounded normal linear operators on a (complex) Hilbert space \(H\), then for each \(\alpha \in (0,1)\) \[ {D}(({\overline{A+B}})^{\alpha}) = {D}(A^{\alpha})\cap {D}(B^{\alpha})= {D}(({\overline{A+B}})^{*\alpha}), \] where \(\overline{A+B}\) denotes the closure of the algebraic sum \(A+B\) of \(A\) and \(B\). This result is applied to characterize the domains of fractional powers of a large class of the Hamiltonians with singular potentials arising in quantum mechanics through the study of the Schrödinger equation.

47B25 Linear symmetric and selfadjoint operators (unbounded)
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
47B44 Linear accretive operators, dissipative operators, etc.
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