Friedrichs extensions of Schroedinger operators with singular potentials

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dc.creatorvon Keviczky, Attila B.
dc.creatorSaad, Nasser
dc.creatorHall, Richard L.
dc.date2003-12-10
dc.date.accessioned2026-07-07T04:30:48Z
dc.date.available2026-07-07T04:30:48Z
dc.descriptionThe Friedrichs extension for the generalized spiked harmonic oscillator given by the singular differential operator -D^2+ Bx^2 + Ax^{-2} + lambda x^{-alpha} (B>0, A >= 0) in L_2(0, infinity) is studied. We look at two different domains of definition for each of these differential operators in L_2(0, infinity), namely C_0^infinity(0, infinity) and D(T_{2,F})\cap D(M_{lambda, alpha}), where the latter is a subspace of the Sobolev space W_{2,2}(0, infinity). Adjoints of these differential operators on C_0^infinity(0,infinity) exist as result of the null-space properties of functionals. For the other domain, convolutions and Jensen and Minkowski integral inequalities, density of C_0^\infinity(0,\infinity) in D(T_{2,F})\cap D(M_{λ, α}) in L_2(0,\infinity) lead to the other adjoints. Further density properties C_0^infinity(0,infinity) on D(T_{2,F})\cap D(M_{λ, α}) yield the Friedrichs extension of these differential operators with domains of definition D(T_{2,F})\cap D(M_{lambda, alpha}).
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0312027
dc.identifierhttp://arxiv.org/abs/math-ph/0312027
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57594
dc.subjectMathematical Physics
dc.titleFriedrichs extensions of Schroedinger operators with singular potentials
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