A survey on uncertainty principles related to quadratic forms
- Autores: Bruno Demange, Aline Bonami
- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 57, Fasc. Extra 1, 2006 (Ejemplar dedicado a: Proceedings of the 7th International Conference on Harmonic Analysis and Partial Differential Equations), págs. 1-36
- Idioma: español
- Enlaces
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Resumen
Hardy¿s Uncertainty Principle may be seen as a characterisation of all tempered distributions f on Rd such that e±qf and e±q0 bf 2 S0(Rd) are also tempered, with q and q0 two positive definite quadratic forms.
After proving this, we consider the same problem for general non degenerate quadratic forms q and q0. A special attention is given to the case when q(x, y) = q0(x, y) = hx, yi on Rd × Rd, for which the results that we describe here may be seen as a generalization of Beurling¿s Uncertainty principle. We also consider other kinds of uncertainty principles related to quadratic forms, which describe strong or weak annihilating pairs in the sense of Havin and J¿oricke.
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