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An inverse problem involving the Titchmarsh–Weyl m-function

Published online by Cambridge University Press:  14 November 2011

B.J. Harris
B.J. Harris
Affiliation:
Department of Mathematics, Northern Illinois University, Dekalb, Illinois 60115, U.S.A.
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Synopsis

Let m(λ) denote the Titchmarsh–Weyl m-function associated with the differential equation

with Neumann boundary condition at 0. In the case q ∊ CM[0, ε) for some integer M and ε > 0 we prove the following result (Theorem 2.1): If for some integer ŋ ≧ 3 we know that Im {λ(ŋ + l)/2m0(λ)} = 0 on the ray λ = |λ| eiπ/ŋ, then q(v) (0) = 0 for all v in the set {0, 1, … M} for Which ≢ ŋ − 2 mod ŋ.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 110 , Issue 3-4 , 1988 , pp. 305 - 309
Copyright
Copyright © Royal Society of Edinburgh 1988

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