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- W2092962005 abstract "Motivated by Heisenberg–Weyl type uncertainty principles for the torusTand the sphereS2due to Breitenberger, Narowich, Ward, and others, we derive an uncertainty relation for radial functions on the spheresSn ⊂ Rn + 1and, more generally, for ultraspherical expansions on [0, π]. In this setting, the “frequency variance” of aL2-function on [0, π] is defined by means of the ultraspherical differential operator, which plays the role of a Laplacian. Our proof is based on a certain first-order differential-difference operator on the doubled interval [−π, π]. Moreover, using the densitiesftof “Gaussian measures” on [0, π] with the timettending to 0, we show that the bound of our uncertainty principle is optimal." @default.
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- W2092962005 title "An Uncertainty Principle for Ultraspherical Expansions" @default.
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- W2092962005 doi "https://doi.org/10.1006/jmaa.1997.5386" @default.
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