Facing linear difference equations through hypergroup methodss

Kristine Ey; Rupert Lasser

doi:10.1080/10236190701388450

Facing linear difference equations through hypergroup methodss

Kristine Ey, Rupert Lasser

Helmholtz Zentrum München German Research Center for Environmental Health

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We investigate a class of second-order linear difference equations by applying results of harmonic analysis on polynomial hypergroups. For the scalar case we show that the solutions are either bounded by the modulus of the initial value or are unbounded. For the Hilbert space-valued case we establish a concrete representation of the solutions whenever they are bounded and stationary. Among various examples we discuss those corresponding to Jacobi polynomials.

Original language	English
Pages (from-to)	953-965
Number of pages	13
Journal	Journal of Difference Equations and Applications
Volume	13
Issue number	10
DOIs	https://doi.org/10.1080/10236190701388450
State	Published - Oct 2007
Externally published	Yes

Keywords

Jacobi polynomials
Linear difference equations
Orthogonal polynomials
Polynomial hypergroups

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10.1080/10236190701388450

Cite this

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abstract = "We investigate a class of second-order linear difference equations by applying results of harmonic analysis on polynomial hypergroups. For the scalar case we show that the solutions are either bounded by the modulus of the initial value or are unbounded. For the Hilbert space-valued case we establish a concrete representation of the solutions whenever they are bounded and stationary. Among various examples we discuss those corresponding to Jacobi polynomials.",

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AB - We investigate a class of second-order linear difference equations by applying results of harmonic analysis on polynomial hypergroups. For the scalar case we show that the solutions are either bounded by the modulus of the initial value or are unbounded. For the Hilbert space-valued case we establish a concrete representation of the solutions whenever they are bounded and stationary. Among various examples we discuss those corresponding to Jacobi polynomials.

KW - Jacobi polynomials

KW - Linear difference equations

KW - Orthogonal polynomials

KW - Polynomial hypergroups

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M3 - Article

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JF - Journal of Difference Equations and Applications

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Facing linear difference equations through hypergroup methodss

Abstract

Keywords

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