𝔖 Bobbio Scriptorium
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Localized functions on a sphere

✍ 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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✦ 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.


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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 HΕ‘rmander type inequality.

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