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Sturm-Liouville Transformation

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Multidimensional Signals and Systems

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Abstract

This chapter revisits the topic of multidimensional transformations and applies it to initial-boundary-value problems. Some basic notions are first discussed by an introductory example. Then the spatial differentiation operators involved in initial-boundary-value problems are investigated further as a prerequisite to the introduction of a suitable spatial transformation, the Sturm-Liouville transformation. The corresponding operations in the space domain are described by Green’s functions and the corresponding propagator. This transformation derived for initial-boundary-value problems with constant coefficients is extended to space-dependent coefficients. The chapter closes which some classical Sturm-Liouville problems.

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Notes

  1. 1.

    Jacques Charles François Sturm (1803–1855), Joseph Liouville (1809–1882)

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Authors and Affiliations

  1. Multimedia Communications and Signal Processing, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Germany

    Rudolf Rabenstein

  2. Digital Communications, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Germany

    Maximilian Schäfer

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  1. Rudolf Rabenstein
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  2. Maximilian Schäfer
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Rabenstein, R., Schäfer, M. (2023). Sturm-Liouville Transformation. In: Multidimensional Signals and Systems. Springer, Cham. https://doi.org/10.1007/978-3-031-26514-3_10

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  • DOI: https://doi.org/10.1007/978-3-031-26514-3_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-26513-6

  • Online ISBN: 978-3-031-26514-3

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