Abstract
In this Chapter we study the analytic structure of Bernoulli systems. Although, in comparison with Chapter 5, the group theory and probability theory will be more in the background, they will still appear regularly. In the analytic vein, important features are: the Rodrigues formula (§1.3), the kernel w (§II) which intertwines the Fock space realizations of Chapters 3 and 5, and the Riccati equation (§§1.4, V). Two integral transforms, the Fourier-Laplace transform and the gamma transform (§4.1) are basic elements of the construction of Bernoulli systems from the point of view of the present chapter.
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© 1993 Springer Science+Business Media Dordrecht
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Feinsilver, P., Schott, R. (1993). Bernoulli Systems. In: Algebraic Structures and Operator Calculus. Mathematics and Its Applications, vol 241. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1648-0_7
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DOI: https://doi.org/10.1007/978-94-011-1648-0_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4720-3
Online ISBN: 978-94-011-1648-0
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