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

We use the methods of Fourier–Jacobi harmonic analysis to study problems of the approximation of functions in weighted L2 function spaces on the half-axis [0,+∞). 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.