Inverse problem for Sturm-Liouville operators with distribution potentials: reconstruction from two spectraстатья
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Дата последнего поиска статьи во внешних источниках: 3 февраля 2015 г.
Аннотация:In this paper, we deal with operators of the form Ly = –y'' + q(x)y, where q Î W2–1[0,p]. Let s be a function such that s' = q, let y[1](x) = y(x) – s(x)y(x), and let the operators LD and LDN be defined by the expression L on the domains
D(LD) = {y, y[1] Î AC | y(0) = y(p) = 0} and D(LDN) = y, y[1] Î AC | y(0) = y[1](p) = 0}, respectively, where AC stands for the class of absolutely continuous functions. We give a complete characterization of sequences {lk}1¥ and {mk}1¥ which can be the spectra of the operators LD and LDN with a potential q(x) Î W2q(0,p) for any fixed q ³ –1, where W2q is the Sobolev space.