An Uncertainty Principle for Ultraspherical Expansions

  title={An Uncertainty Principle for Ultraspherical Expansions},
  author={Margit Rr Osler and Michael Voit},
Motivated by Heisenberg-Weyl type uncertainty principles for the torus T and the sphere S 2 due to Breitenberger, Narcowich, Ward and others, we derive an uncertainty relation for radial functions on the spheres S n IR n+1 and, more generally, for ultras-pherical expansions on 0; ]: In this setting, the \frequency variance" of a L 2-function on 0; ] is deened by means of the ultraspherical diierential operator, which plays the role of a Laplacian. Our proof is based on a certain rst-order… CONTINUE READING


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