Name
Title | ||
|---|---|---|
Polynomial operators and local approximation of solutions of pseudo-differential equations on the sphere |
Abstract | ||
|---|---|---|
We study the solutions of an equation of the form Lu=f, where L is a pseudo-differential operator defined for functions on the unit sphere embedded in a Euclidean space, f is a given function, and u is the desired solution. We give conditions under which the solution exists, and deduce local smoothness properties of u given corresponding local smoothness properties of f, measured by local Besov spaces. We study the global and local approximation properties of the spectral solutions, describe a method to obtain approximate solutions using values of f at points on the sphere and polynomial operators, and describe the global and local rates of approximation provided by our polynomial operators. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1007/s00211-006-0676-z | Numerische Mathematik |
Keywords | Field | DocType |
differential equation,pseudo differential operator,besov space,approximation property,euclidean space | Spectral properties,Differential equation,Polynomial,Mathematical analysis,Euclidean space,Operator (computer programming),Numerical analysis,Smoothness,Mathematics,Unit sphere | Journal |
Volume | Issue | ISSN |
103 | 2 | 0945-3245 |
Citations | PageRank | References |
4 | 0.60 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Q. T. Le Gia | 1 | 93 | 12.64 |
| Hrushikesh Narhar Mhaskar | 2 | 257 | 61.07 |