A Galoisian Approach to Complex Oscillation Theory

Guofu Yu; Yik Man Chiang

A Galoisian Approach to Complex Oscillation Theory

Department of Mathematics

Research output: Contribution to conference › Conference Paper

Abstract

We demonstrate that complex non-oscillatory solutions (in the sense of Nevanlinna theory) of certain class of Hill equations are among the Liouvillian solutions of associated differential equations. We shall establish a full equivalence between the two viewpoints when the Hill potential is a linear combination of four exponential functions. This equation is closely related to the classical Lame and Mathieu equations. We shall also discuss new orthogonality found for these non-oscillatory solutions.

Original language	English
Publication status	Published - Jul 2016
Event	The 11th AIMS Conference on Dynamical Dynamical Systems, Differential Equations and Applications - Duration: 1 Jul 2016 → 1 Jul 2016

Conference

Conference	The 11th AIMS Conference on Dynamical Dynamical Systems, Differential Equations and Applications
Period	1/07/16 → 1/07/16

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https://hdl.handle.net/1783.1/87277

Cite this

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title = "A Galoisian Approach to Complex Oscillation Theory",

abstract = "We demonstrate that complex non-oscillatory solutions (in the sense of Nevanlinna theory) of certain class of Hill equations are among the Liouvillian solutions of associated differential equations. We shall establish a full equivalence between the two viewpoints when the Hill potential is a linear combination of four exponential functions. This equation is closely related to the classical Lame and Mathieu equations. We shall also discuss new orthogonality found for these non-oscillatory solutions.",

author = "Guofu Yu and Chiang, \{Yik Man\}",

year = "2016",

month = jul,

language = "English",

note = "The 11th AIMS Conference on Dynamical Dynamical Systems, Differential Equations and Applications ; Conference date: 01-07-2016 Through 01-07-2016",

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TY - CONF

T1 - A Galoisian Approach to Complex Oscillation Theory

AU - Yu, Guofu

AU - Chiang, Yik Man

PY - 2016/7

Y1 - 2016/7

N2 - We demonstrate that complex non-oscillatory solutions (in the sense of Nevanlinna theory) of certain class of Hill equations are among the Liouvillian solutions of associated differential equations. We shall establish a full equivalence between the two viewpoints when the Hill potential is a linear combination of four exponential functions. This equation is closely related to the classical Lame and Mathieu equations. We shall also discuss new orthogonality found for these non-oscillatory solutions.

AB - We demonstrate that complex non-oscillatory solutions (in the sense of Nevanlinna theory) of certain class of Hill equations are among the Liouvillian solutions of associated differential equations. We shall establish a full equivalence between the two viewpoints when the Hill potential is a linear combination of four exponential functions. This equation is closely related to the classical Lame and Mathieu equations. We shall also discuss new orthogonality found for these non-oscillatory solutions.

M3 - Conference Paper

T2 - The 11th AIMS Conference on Dynamical Dynamical Systems, Differential Equations and Applications

Y2 - 1 July 2016 through 1 July 2016

ER -

A Galoisian Approach to Complex Oscillation Theory

Abstract

Conference

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