Abstract
The complex point of view opens wide prospects for our theme: in its different manifestations the uncertainty principle arises as a corollary of the various uniqueness theorems in which complex analysis is so rich. Here is a crude example: the fact that any charge μ ε M (ℝ) with bounded support and bounded spectrum vanishes identically follows immediately from the fact that µ coincides on ℝ with some entire function if diam supp µ < +∞. It is clear that this primitive consideration can be developed into much more precise results.
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© 1995 Springer-Verlag Berlin Heidelberg
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Havin, V.P., Nikol’skij, N.K. (1995). Complex Methods. In: Havin, V.P., Nikol’skij, N.K. (eds) Commutative Harmonic Analysis III. Encyclopaedia of Mathematical Sciences, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57854-0_13
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DOI: https://doi.org/10.1007/978-3-642-57854-0_13
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