Abstract
The present paper extends Stetkær’s Algebraic Small Dimension Lemma on semigroups (Stetkær in Aequat Math, 2020) by replacing its involution by an anti-homomorphism that need not be involutive. We apply our result, to give an accessible approach to solve the d’Alembert \( \mu \)-functional equation and the Wilson \(\mu \)-functional equation on compact groups with an anti-homomorphism. This generalizes Yang’s result (Yang in Canad Math Bull 56: 218–224, 2013).
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Acknowledgements
Our sincere regards and gratitude go to Professor Henrik Stetkær for fruitful discussions and for valuable comments.
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Ayoubi, M., Zeglami, D. The Algebraic Small Dimension Lemma with an Anti-Homomorphism on Semigroups. Results Math 76, 66 (2021). https://doi.org/10.1007/s00025-021-01377-7
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DOI: https://doi.org/10.1007/s00025-021-01377-7
Keywords
- Functional equation
- d’Alembert
- non-abelian Fourier transform
- anti-homomorphism
- irreducible representation
- semigroup