Advances in Differential Equations

Transformation theory of symmetric differential expressions

Horst Behncke and Don Hinton

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Abstract

We consider the problem of transforming a symmetric differential expression of even or odd order with both real and complex coefficients with a Kummer-Liouville transformation. An existence proof is given which yields an algorithm for computing exactly the coefficients of the transformed equation. By using the concept of a modified Kummer-Liouville transformation we derive explicit expressions for the coefficients of the transformed equation which are correct modulo Levinson terms only. However, the application of Levinson's theorem to asymptotic integration shows that Levinson terms have no effect on the asymptotics of the eigenfunctions.

Article information

Source
Adv. Differential Equations Volume 11, Number 6 (2006), 601-626.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867687

Mathematical Reviews number (MathSciNet)
MR2238021

Zentralblatt MATH identifier
1099.34073

Subjects
Primary: 34A30: Linear equations and systems, general
Secondary: 34C20: Transformation and reduction of equations and systems, normal forms 34L05: General spectral theory 34L20: Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions 47E05: Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number in section 47)

Citation

Behncke, Horst; Hinton, Don. Transformation theory of symmetric differential expressions. Adv. Differential Equations 11 (2006), no. 6, 601--626. https://projecteuclid.org/euclid.ade/1355867687.


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