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» LAGO on the unit sphere
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NA
2007
81views more  NA 2007»
13 years 7 months ago
Positive weight quadrature on the sphere and monotonicities of Jacobi polynomials
In 2000, Reimer proved that a positive weight quadrature rule on the unit sphere Sd ⊂ Rd+1 has the property of quadrature regularity. Hesse and Sloan used a related property, ca...
Paul C. Leopardi
JC
2007
64views more  JC 2007»
13 years 7 months ago
Quadrature in Besov spaces on the Euclidean sphere
Let q ≥ 1 be an integer, Sq denote the unit sphere embedded in the Euclidean space Rq+1, and µq be its Lebesgue surface measure. We establish upper and lower bounds for sup fâˆ...
Kerstin Hesse, H. N. Mhaskar, Ian H. Sloan
CPC
2007
112views more  CPC 2007»
13 years 7 months ago
Graphs with Large Girth Not Embeddable in the Sphere
In 1972, M. Rosenfeld asked if every triangle-free graph could be embedded in the unit sphere Sd in such a way that two vertices joined by an edge have distance more than √ 3 (i...
Pierre Charbit, Stéphan Thomassé
ADCM
2004
74views more  ADCM 2004»
13 years 7 months ago
Extremal Systems of Points and Numerical Integration on the Sphere
This paper considers extremal systems of points on the unit sphere Sr Rr+1, related problems of numerical integration and geometrical properties of extremal systems. Extremal sys...
Ian H. Sloan, Robert S. Womersley
ADCM
2000
57views more  ADCM 2000»
13 years 7 months ago
Polynomial frames on the sphere
We introduce a class of polynomial frames suitable for analyzing data on the surface of the unit sphere of a Euclidean space. Our frames consist of polynomials, but are well local...
Hrushikesh Narhar Mhaskar, Francis J. Narcowich, J...