Symmetrical Differential Operators and Their Friedrichs Extension
نویسندگان
چکیده
منابع مشابه
Unbounded operators, Friedrichs’ extension theorem
Explicit naming of the domain of an unbounded operator is often suppressed, instead writing T1 ⊂ T2 when T2 is an extension of T1, in the sense that the domain of T2 contains that of T1, and the restriction of T2 to the domain of T1 agrees with T1. An operator T ′, D′ is a sub-adjoint to an operator T,D when 〈Tv,w〉 = 〈v, T ′w〉 (for v ∈ D, w ∈ D′) For D dense, for given D′ there is at most one T...
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In this note, by A ⊂ B, I mean that A is contained in B, and it may be that A = B; usually I write this by A ⊆ B, but A ⊂ B fits with the usual notation for saying that an operator is an extension of another. In this note, unless we say otherwise H denotes a Hilbert space over C, and we do not presume H to be separable. We shall write the inner product 〈·, ·〉 on H as conjugate linear in the sec...
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Problems of existence of the singular spectrum on the continuous spectrum emerges in some mathematical aspects of quantum scattering theory and quantum solid physics. In the latter field, this phenomenon results from physical effects such as the Anderson transitions in dielectrics. In the study of this problem, selfadjoint Friedrichs model operators play an important part and constitute quite a...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1995
ISSN: 0022-0396
DOI: 10.1006/jdeq.1995.1003