International Journal of Analysis and Applications | 2026
Authors: Shadimetov Kh.M.; Jalolov O.I.
DOI: 10.28924/2291-8639-24-2026-134
Journal: International Journal of Analysis and Applications
Year: 2026
Publisher: Etamaths Publishing
Document Type: Article
Open Access: All Open Access; Gold Open Access
Cited by: 0
In investigating various problems related to the theory of approximate integration, partial differential equations, and other areas of analysis, the functional approach has proven to be highly effective. This approach involves treating the differential equation with boundary conditions as an operator acting in a specifically chosen functional space. The necessary information is derived from the properties of this operator. When addressing problems in approximate integration and differential equations, the appropriate selection of functional spaces is crucial for success. S.L. Sobolev exemplified this method clearly in his well-known study of polyharmonic equations. In our research, we examined cubature formulas within the Sobolev functional space ¯L(m) p (Sn ) for functions defined on n-dimensional unit sphere S. This issue requires careful attention when developing the most efficient formulas. In this paper, we discussed formulas that fulfill this criterion and refered to them as “practical” in accordance with N.S. Bakhvalov’s terminology. © 2026 the author(s).
cubature formula; error functional; extremal function; functional space; generalized function; norm