Spaces of Analytic Functions

Hemant Kumar Pathak ()
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Hemant Kumar Pathak: Pt. Ravishankar Shukla University, School of Studies in Mathematics

Chapter Chapter 8 in Complex Analysis and Applications, 2019, pp 625-648 from Springer

Abstract: Abstract In this chapter, we shall put a metric on the set of all analytic functions on a fixed region $$G\subset \mathbb {C},$$ and “compactness”, “converge”, “normality”, “uniform continuity”, and “equicontinuity” in this metric space is discussed. We shall alsoEquicontinuity discuss Hurwitz’s theorem, Montel’s theorem and Montel’s theorem among the applications obtained is a proof ofRiemann mapping theorem the Riemann mapping theorem.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-13-9734-9_8

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DOI: 10.1007/978-981-13-9734-9_8

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