Some problems in the theory of approximation of functions on compact homogeneous manifolds

Journal Article · Tue Jun 30 00:00:00 EDT 2009 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2009V200N06ABEH004021; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21301614

Platonov, Sergei S ^[1]

---

1. Petrozavodsk State University, Petrozavodsk (Russian Federation)

Problems in the theory of approximation of functions on an arbitrary compact rank-one symmetric space M in the metric of L{sub p}, 1{<=}p{<=}{infinity}, are investigated. The approximating functions are generalized spherical polynomials, that is, linear combinations of eigenfunctions of the Beltrami-Laplace operator on M. Analogues of the direct Jackson theorems are proved for the modulus of smoothness (of arbitrary order) constructed by using the operator of spherical averaging. It is established that the modulus of smoothness and the K-functional constructed from the Sobolev-type space corresponding to the Beltrami-Laplace differential operator are equivalent. Bibliography: 35 titl0008.

• OSTI ID: 21301614
• Journal Information: Sbornik. Mathematics, Vol. 200, Issue 6; Other Information: DOI: 10.1070/SM2009v200n06ABEH004021; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
APPROXIMATIONS
EIGENFUNCTIONS
LAPLACIAN
MATHEMATICAL SPACE
METRICS
POLYNOMIALS
ROUGHNESS
SMOOTH MANIFOLDS
SPHERICAL CONFIGURATION
SYMMETRY