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Erlangen Program at Large: An Overview

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Advances in Applied Analysis

Part of the book series: Trends in Mathematics ((TM))

Abstract

This is an overview of the Erlangen Program at Large. Study of objects and properties, which are invariant under a group action, is very fruitful far beyond traditional geometry. In this paper we demonstrate this on the example of the group SL2(ℝ). Starting from the conformal geometry we develop analytic functions and apply these to functional calculus. Finally we link this to quantum mechanics and conclude by a list of open problems.

Mathematics Subject Classification (2010). Primary 30G35; Secondary 22E46, 30F45, 32F45, 43A85, 30G30, 42C40, 46H30, 47A13, 81R30, 81R60.

A mathematical idea should not be petrified in a formalised axiomatic setting, but should be considered instead as flowing as a river.

Sylvester (1878)

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Authors and Affiliations

  1. School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK

    Vladimir V. Kisil

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  1. Vladimir V. Kisil
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Correspondence to Vladimir V. Kisil .

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  1. , Department of Economics, Belarusian State University, Nezavisimosti ave 4, Minsk, 220030, Belarus

    Sergei V. Rogosin

  2. , Department of Economics, Belarus State University, Nezavisimosti ave 4, Minsk, 220030, Belarus

    Anna A. Koroleva

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Dedicated to Prof. Hans G. Feichtinger on the occasion of his 60th birthday

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Kisil, V.V. (2012). Erlangen Program at Large: An Overview. In: Rogosin, S., Koroleva, A. (eds) Advances in Applied Analysis. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0417-2_1

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