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Factorization of disconjugate higher-order Sturm-Liouville difference operators

✍ Scribed by O. Dosˇlý

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
400 KB
Volume
36
Category
Article
ISSN
0898-1221

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✦ Synopsis

Using a recently proved equivalence between disconjugacy of the 2nth-order difference equation tt v--'--O and solvability of the correeponding Riccati matrix difference equation, it is shown that the equation L(I/) = 0 is di~onjugate on a given interval if and only if the operator L admits the factoriz&tion of the form

L(Y)k+n = M* (ckM(y)k)k+n,

where M and its adjoint M* are certain nth-order difference operators and ch is a sequence of positive numbers.

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Spectral theory of Sturm–Liouville diffe
Spectral theory of Sturm–Liouville difference operators
✍ Guoliang Shi; Hongyou Wu 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 241 KB

We present several classes of explicit self-adjoint Sturm-Liouville difference operators with either a non-Hermitian leading coefficient function, or a non-Hermitian potential function, or a non-definite weight function, or a non-self-adjoint boundary condition. These examples are obtained using a g