Geodesic
Polynomials of Least Deviation from Zero and Chebyshev-Type Cubature Formulas
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 45-57

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The problem about a polynomial of least deviation from zero on a multidimensional sphere is solved in some special cases. For known spherical configurations, a family of subspaces of harmonic polynomials is described for which the Chebyshev-type cubature formulas on the sphere are exact. 
@article{TM_2001_232_a6,
     author = {N. N. Andreev and V. A. Yudin},
     title = {Polynomials of {Least} {Deviation} from {Zero} and {Chebyshev-Type} {Cubature} {Formulas}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {45--57},
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     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2001_232_a6/}
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N. N. Andreev; V. A. Yudin. Polynomials of Least Deviation from Zero and Chebyshev-Type Cubature Formulas. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 45-57. http://geodesic.mathdoc.fr/item/TM_2001_232_a6/