Non-harmonic cones are sets of injectivity for the twisted spherical means on \(\mathbb {C}^n\) (Q2787961)
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scientific article; zbMATH DE number 6550640
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Non-harmonic cones are sets of injectivity for the twisted spherical means on \(\mathbb {C}^n\) |
scientific article; zbMATH DE number 6550640 |
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7 March 2016
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spherical harmonics
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Heisenberg group
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twisted convolution
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set of injectivity
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Non-harmonic cones are sets of injectivity for the twisted spherical means on \(\mathbb {C}^n\) (English)
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The author proves that a complex cone \(C\) is a set of injectiviy for the twisted spherical means for the class of all continuous functions on \(\mathbb C^n( n \geq 2)\) if and only if \(C\) does not completely lay on the level surface of any bi-graded homogeneous harmonic polynomial on \(\mathbb C^n\). Further, the author produces examples of such level surfaces.
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