Differential and Integral Equations

A class of differential operators with complex coefficients and compact resolvent

Horst Behncke and Don Hinton

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We consider the problem of the a second order singular differential operator with complex coefficients in the discrete spectrum case. The Titchmarsh-Weyl m-function is constructed without the use of nesting circles, and it is then used to give a representation of the resolvent operator. Under conditions on the growth of the coefficients, the resolvent operator is proved to be Hilbert-Schmidt and the root subspaces are shown to be complete in the associated Hilbert space. The operator is considered on both the half line and whole line cases.

Article information

Differential Integral Equations, Volume 31, Number 5/6 (2018), 375-402.

First available in Project Euclid: 23 January 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34L05: General spectral theory 34L10: Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions 34B20: Weyl theory and its generalizations 34B24: Sturm-Liouville theory [See also 34Lxx] 34B27: Green functions 34B60: Applications


Behncke, Horst; Hinton, Don. A class of differential operators with complex coefficients and compact resolvent. Differential Integral Equations 31 (2018), no. 5/6, 375--402. https://projecteuclid.org/euclid.die/1516676435

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