Spectral analysis of a self-similar Sturm-Liouville operator
نویسندگان
چکیده
منابع مشابه
Spectral analysis of a self-similar Sturm-Liouville operator
In this text we describe the spectral nature (pure point or continuous) of a self-similar Sturm-Liouville operator on the line or the half-line. This is motivated by the more general problem of understanding the spectrum of Laplace operators on unbounded finitely ramified self-similar sets. In this context, this furnishes the first example of a description of the spectral nature of the operator...
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We consider the Sturm-Liouville operator Lu = u ′′ − q(x)u defined on (0, π) with regular but not strongly regular boundary conditions. Under some supplementary assumptions we prove that the set of potentials q(x) that ensure an asymptotically multiple spectrum is everywhere dense in L 1 (0, π). In the present paper we consider eigenvalue problems for the Sturm-Liouville equation u ′′ − q(x)u +...
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2005
ISSN: 0022-2518
DOI: 10.1512/iumj.2005.54.2490