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Entire Solutions of the Hille-Type Functional Equation

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Functional Equations and Inequalities

Part of the book series: Mathematics and Its Applications ((MAIA,volume 518))

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Abstract

Let f, g, h be unknown entire functions of a complex variable and let s, t be real variables. We deal with the generalization of Hille’s functional equation

$\left| {f(s + it)} \right| = \left| {g(s)} \right| + \left| {h(it)} \right|.$

The main goal of the paper is to determine all entire solutions f,g,h, of the above equation.

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References

  1. J. Aczél, H. Haruki, Commentary to Einar Hille’s collected works, MIT Press, (1975), 651–658.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Pedagogical University, Podchorążych 2, PL-30-084, Kraków, Poland

    Andrzej Smajdor

  2. Institute of Mathematics, Silesian University, Bankowa 14, PL-40-007, Katowice, Poland

    Wilhelmina Smajdor

Authors
  1. Andrzej Smajdor
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  2. Wilhelmina Smajdor
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© 2000 Springer Science+Business Media Dordrecht

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Smajdor, A., Smajdor, W. (2000). Entire Solutions of the Hille-Type Functional Equation. In: Functional Equations and Inequalities. Mathematics and Its Applications, vol 518. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4341-7_20

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  • DOI: https://doi.org/10.1007/978-94-011-4341-7_20

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5869-8

  • Online ISBN: 978-94-011-4341-7

  • eBook Packages: Springer Book Archive

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