A Beurling-Helson type theorem for modulation spaces
We prove a Beurling-Helson type theorem on modulation spaces. More precisely, we show that the only 𝒞1 changes of variables that leave invariant the modulation spaces ℳp,q(ℝd) are affine functions on ℝd. A special case of our result involving the Sjöstrand algebra was considered earlier by A. Boulkh...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2009-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/956891 |
| Summary: | We prove a Beurling-Helson type theorem on modulation spaces.
More precisely, we show that the only 𝒞1 changes of variables that leave invariant
the modulation spaces ℳp,q(ℝd) are affine functions on ℝd. A special case of our
result involving the Sjöstrand algebra was considered earlier by A. Boulkhemair. |
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| ISSN: | 0972-6802 |