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Characterization of domains of self-adjoint ordinary differential operators. II. (English) Zbl 1290.47046

The paper under review characterizes the self-adjoint domains associated with an even order (\(n = 2k\)) linear (symmetric) ordinary differential expression with real valued coefficients, considered on \(J = (a,b)\), \(-\infty \leq a < b \leq \infty\). The authors study the case when both end points \(a\) and \(b\) are singular and all possible values for the deficiency index \(d\) (\(0 \leq d \leq n\)) are considered. Using an arbitrary interior point \(c\) and the approach of Part I [the last three authors, J. Differ. Equations 246, No. 4, 1600–1622 (2009; Zbl 1169.47033)], the characterization of self-adjoint domains is obtained in terms of the LC solutions on \((a,c)\) and on \((c,b)\). The characterizations obtained are hoped to “lead to a canonical form for self-adjoint boundary conditions such as the well known form in the second order case”. A thorough introduction on the theme of the paper and an extensive list of references are included.

MSC:

47E05 General theory of ordinary differential operators
34B20 Weyl theory and its generalizations for ordinary differential equations
34B24 Sturm-Liouville theory
47B25 Linear symmetric and selfadjoint operators (unbounded)

Citations:

Zbl 1169.47033
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References:

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