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On a property of functions on the sphere and its application

✍ Scribed by Yuhong Liu


Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
247 KB
Volume
73
Category
Article
ISSN
0362-546X

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πŸ“œ SIMILAR VOLUMES


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✍ D. Rees; G. G. Hall πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 692 KB

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

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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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✍ Frank Baginski πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 438 KB

A function which is homogeneous in x y z of degree n and satisfies V xx + V yy + V zz = 0 is called a spherical harmonic. In polar coordinates, the spherical harmonics take the form r n f n , where f n is a spherical surface harmonic of degree n. On a sphere, f n satisfies f n + n n + 1 f n = 0, whe