Modulus of Smoothness and Approximation Theorems in Clifford Analysis
- Resource Type
- Original Paper
- Authors
- Tyr, Othman
- Source
- Complex Analysis and Operator Theory. 18(1)
- Subject
- Clifford algebras
Clifford-Fourier transform
Sobolev-type space
K-functionals
Modulus of smoothness
42B10
42A38
43A62
- Language
- English
- ISSN
- 1661-8254
1661-8262
This paper uses some basic results on Clifford analysis introduced by E. Hitzer, to study some problems in the theory of approximation of functions in the space of square integral functions in the Clifford algebra. The equivalence between the moduli of smoothness of all orders constructed by the Steklov function and the K-functionals constructed from the Sobolev-type space is proved. A consequence of this equivalence theorem is given at the end of this work.