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Preliminaries

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Convolution-like Structures, Differential Operators and Diffusion Processes

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2315))

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Abstract

Our opening discussion in the introductory chapter sketched some connections between the problem of constructing generalized convolutions and various fields of mathematics such as harmonic analysis, stochastic processes, differential equations, spectral theory and special functions. In the first three sections of this chapter, we review some prerequisite notions and facts from these fields. Section 2.4 closes the chapter with an example of a generalized convolution (the Kingman convolution), providing motivation and a benchmark for the results in further chapters.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, University of Porto, Porto, Portugal

    Rúben Sousa & Semyon Yakubovich

  2. Department of Mathematics, ISEG, Universidade de Lisboa, Lisbon, Portugal

    Manuel Guerra

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  1. Rúben Sousa
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  2. Manuel Guerra
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  3. Semyon Yakubovich
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Sousa, R., Guerra, M., Yakubovich, S. (2022). Preliminaries. In: Convolution-like Structures, Differential Operators and Diffusion Processes. Lecture Notes in Mathematics, vol 2315. Springer, Cham. https://doi.org/10.1007/978-3-031-05296-5_2

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