Abstract
The construction of novel Fourier/Mellin-type transform pairs that are tailor-made for given planar regions within the special class of circular domains is surveyed. Circular domains are those having boundary components that are either circular arcs or straight lines. The new transform pairs generalize the classical Fourier and Mellin transforms. These geometry-fitted transform pairs can be used to great advantage in solving boundary value problems defined in these domains.
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Acknowledgments
The author acknowledges the support of an Established Career Fellowship from the Engineering and Physical Sciences Research Council in the UK (EP/K019430/1) and a Wolfson Research Merit Award from the Royal Society.
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Crowdy, D. (2016). Geometry-Fitted Fourier-Mellin Transform Pairs. In: Qian, T., Rodino, L. (eds) Mathematical Analysis, Probability and Applications – Plenary Lectures. ISAAC 2015. Springer Proceedings in Mathematics & Statistics, vol 177. Springer, Cham. https://doi.org/10.1007/978-3-319-41945-9_2
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DOI: https://doi.org/10.1007/978-3-319-41945-9_2
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