Abstract noncommutative Fourier series on \(\Gamma\setminus SE(2)\) (Q2074850)
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scientific article; zbMATH DE number 7472403
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Abstract noncommutative Fourier series on \(\Gamma\setminus SE(2)\) |
scientific article; zbMATH DE number 7472403 |
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Abstract noncommutative Fourier series on \(\Gamma\setminus SE(2)\) (English)
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11 February 2022
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This paper deals with abstract noncommutative harmonic analysis on the right coset space \(\Gamma\setminus SE(2)\) where \(\Gamma\) is a discrete co-compact subgroup of \(SE(2)\), the special Euclidean group in dimension 2. Using a Weil's formula, the authors construct a Fourier series that stands for a reconstruction formula for some complex functions defined on \(\Gamma\setminus SE(2)\). Also, a convolution product is defined and a Plancherel type theorem is established.
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special Euclidean group
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non-commutative Fourier series
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coset space
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discrete subgroup
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crystallographic subgroup
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0.7320729494094849
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0.7270851731300354
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0.725449800491333
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