Fourier–Jacobi harmonic analysis and some problems of approximation of functions on the half-axis in L₂ metric: Nikol'skii–Besov type function spaces

ABSTRACT

We use the methods of Fourier–Jacobi harmonic analysis to study problems of the approximation of functions in weighted $L_2$ function spaces on the half-axis $[0,+\mathrm{\infty })$. 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.

KEYWORDS:

• Fourier–Jacobi harmonic analysis
• approximation of functions
• generalized moduli of smoothness
• Jacobi generalized translation
• Nikol'skii–Besov type function spaces
• Bernstein-type inequalities

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 33C45
• 41A17
• 46E35
• 44A20

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.