The Cauchy Transform of the Square Root Function on the Circle

Raymond Mortini () and Rudolf Rupp ()
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Raymond Mortini: CNRS, Université de Lorraine, Département de Mathématiques et Institut Élie Cartan de Lorraine
Rudolf Rupp: Technische Hochschule Nürnberg, Georg Simon Ohm, Fakultät für Angewandte Mathematik, Physik und Allgemeinwissenschaften

A chapter in Multivariable Operator Theory, 2023, pp 575-586 from Springer

Abstract: Abstract In this note, which is aimed at students and their teachers in a complex analysis course, we calculate with various methods the explicit value of the Cauchy-integrals $$\int _{|z|=1} \sqrt{z} /(z-a)\, dz$$ ∫ | z | = 1 z / ( z - a ) d z for several branches of the square root function. The case $$|a|=1$$ | a | = 1 involves the notion of the Cauchy principal value.

Keywords: Cauchy integral; Square root function; Arcus tangens; Primary 30-01; Secondary 30D10 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-50535-5_23

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DOI: 10.1007/978-3-031-50535-5_23

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