Solution of a functional equation on compact groups using Fourier analysis
2015 ◽
Vol 69
(2)
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pp. 9
Keyword(s):
Let \(G\) be a compact group, let \(n \in N\setminus \{0,1\}\) be a fixed element and let \(\sigma\) be a continuous automorphism on \(G\) such that \(\sigma^n=I\). Using the non-abelian Fourier transform, we determine the non-zero continuous solutions \(f:G \to C\) of the functional equation \[ f(xy)+\sum_{k=1}^{n-1}f(\sigma^k(y)x)=nf(x)f(y),\ x,y \in G,\] in terms of unitary characters of \(G\).
Keyword(s):
1996 ◽
Vol 119
(4)
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pp. 657-663
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2015 ◽
Vol 93
(3)
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pp. 467-472
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2003 ◽
Vol 10
(3)
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pp. 503-508
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1985 ◽
Vol 98
(2)
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pp. 195-212
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2013 ◽
Vol 56
(1)
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pp. 218-224
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1974 ◽
Vol 17
(3)
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pp. 274-284
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