We prove that a class of invariant functions, admissible with respect to the Fubini-Study metric on the sphere S 2 = P 1 C are bounded from below by a function going to infinity on the intersection of charts. This lower bound is sharp in terms of an HΕrmander type inequality.
Localized functions on a sphere
β Scribed by D. Rees; G. G. Hall
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 692 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0020-7608
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β¦ Synopsis
This article provides a fully consistent group theoretical procedure for finding atomic hybrids on a sphere and for relating them to the matrices representing the operators x, y, and z with respect to given basis functions. The tetrahedral, octahedral, and cubic hybrids based on the cube are derived. These functions are localized and directional. They can be used to describe valence aspects of atoms.
π SIMILAR VOLUMES
We study the exponential functional equation f (x + y) = f (x)f (y) on spheres in real normed linear spaces. Regardless of the solutions of this equation, which are already known, we investigate its stability and consider the pexiderized version of it.