ABSTRACT
We use the methods of Fourier–Jacobi harmonic analysis to study problems of the approximation of functions in weighted function spaces on the half-axis . We define function spaces of Nikol'skii–Besov type and describe them in terms of best approximations. We use as the approximation tool a class of functions with the bounded spectrum, that is a class of functions for which their Fourier–Jacobi transform are functions with compact support.
Acknowledgments
The author would like to thank the referee for his valuable suggestions.
Disclosure statement
No potential conflict of interest was reported by the author.