Heisenberg uniqueness pairs and a theorem of Beurling and Malliavin. (English) Zbl 1210.42022
Summary: Let \(\mathbb T\) denote the unit circle in the plane. For various simple sets \(\varLambda \) in the plane we shall study the question whether \((\mathbb T, \varLambda)\) is a Heisenberg uniqueness pair. For example, we shall consider the cases where \(\varLambda \) is a circle or a union of two straight lines. We shall also use a theorem of Beurling and Malliavin.
MSC:
| 42B10 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
References:
| [1] | Havin, V.; Jöricke, B., The Uncertainty Principle in Harmonic Analysis, Ergeb. Math. Grenzgeb. (3), vol. 28 (1994), Springer-Verlag · Zbl 0827.42001 |
| [2] | H. Hedenmalm, A. Montes-Rodríguez, Heisenberg uniqueness pairs and the Klein-Gordon equation, Ann. of Math., in press.; H. Hedenmalm, A. Montes-Rodríguez, Heisenberg uniqueness pairs and the Klein-Gordon equation, Ann. of Math., in press. · Zbl 1227.42002 |
| [3] | Stein, E. M.; Weiss, G., Introduction to Fourier Analysis on Euclidean Spaces (1971), Princeton Univ. Press · Zbl 0232.42007 |
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