Second order differential operators and Dirichlet integrals with singular coefficients, I. Functional calculus of one-dimensional operators
نویسندگان
چکیده
منابع مشابه
Estimates on Green functions of second order differential operators with singular coefficients
We investigate the Green’s functions G(x;x′) of some second order differential operators on R with singular coefficients depending only on one coordinate x0. We express the Green’s functions by means of the Brownian motion. Applying probabilistic methods we prove that when x = (0,x) and x′ = (0, x′) (here x0 = 0) lie on the singular hyperplanes then G(0,x; 0, x′) is more regular than the Green’...
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singular. Under the assumption that Imq(x) ≤ 0 for all x ∈ [a, b), Sims proved that for λ ∈ C+, there exists at least one solution of (1. 1) which lies in the weighted space L(a, b; Im[λ− q]dx); such a solution lies in L(a, b). There are now three distinct possibilities for λ ∈ C+: (I) there is, up to constant multiples, precisely one solution of (1. 1) in L(a, b; Im[λ−q]dx) and L(a, b), (II) o...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1987
ISSN: 0040-8735
DOI: 10.2748/tmj/1178228238