Titlebook: A Discrete Hilbert Transform with Circle Packings; Dominik Volland Book 2017 Springer Fachmedien Wiesbaden GmbH 2017 circle packings.Hilbe

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Agriculture and Internationl RelationsThis chapter introduces our notation conventions and gives a short overview over some results that will be used without references throughout the book.

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https://doi.org/10.1007/978-1-349-07981-0Most of the theory discussed in this chapter will be presented without any proofs. For proofs, we refer to the respective textbooks. The theory of Hardy spaces can be found in the books of Duren [10], Koosis [14] and Hoffman [13]. A more recent book with an emphasis on representation theorems is by Mashreghi [20].

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For an Analytical Political EconomyWe will now turn to the discrete setting and discuss the theory of circle packings.

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2625-3577 nterpart to the Hilbert transform in the realm of a nonlinear discrete complex analysis given by circle packings. The Hilbert transform is closely related to Riemann-Hilbert problems which have been studied in the framework of circle packings by E. Wegert and co-workers since 2009. The author demons

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Book 2017s by E. Wegert and co-workers since 2009. The author demonstrates that the discrete Hilbert transform is well-defined in this framework by proving a conjecture on discrete problems formulated by Wegert. Moreover, he illustrates its properties by carefully chosen numerical examples..

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Book 2017en by circle packings. The Hilbert transform is closely related to Riemann-Hilbert problems which have been studied in the framework of circle packings by E. Wegert and co-workers since 2009. The author demonstrates that the discrete Hilbert transform is well-defined in this framework by proving a c