Boundary triples and Weyl m-functions for powers of the Jacobi differential operator

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Frymark, Dale¹ 

[1] Stockholm Univ, Dept Math, Kraftriket 6, S-10691 Stockholm, Sweden

关键词: Boundary triples;    Self-adjoint extension theory;    Singular Sturm-Liouville operators;    Nevanlinna-Herglotz;    functions;    Weyl m-functions;   

DOI  :  10.1016/j.jde.2020.05.032

来源: Elsevier

【 摘 要 】

The abstract theory of boundary triples is applied to the classical Jacobi differential operator and its powers in order to obtain the Weyl m-function for several self-adjoint extensions with interesting bound- ary conditions: separated, periodic and those that yield the Friedrichs extension. These matrix-valued Nevanlinna-Herglotz m-functions are, to the best knowledge of the author, the first explicit examples to stem from singular higher-order differential equations. The creation of the boundary triples involves taking pieces, determined in [26], of the principal and non-principal solutions of the differential equation and putting them into the sesquilinear form to yield maps from the maximal domain to the boundary space. These maps act like quasi-derivatives, which are usually not well-defined for all functions in the maximal domain of singular expressions. However, well- defined regularizations of quasi-derivatives are produced by putting the pieces of the non-principal solutions through a modified Gram-Schmidt process. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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