Convolution operator singular integral rate of convergence degree of approximation K-functional homogeneous Banach space of periodic functions Fourier transform
Bulgarian Academy of Sciences - National Committee for Mathematics
Mathematica Balkanica New Series, Vol. 25, Fasc 1-2 (2011), 39p-59p
The paper is concerned with establishing direct estimates for convolution operators on homogeneous Banach spaces of periodic functions by means of appropriately defined Kfunctional. The differential operator in the K-functional is defined by means of strong limit and described explicitly in terms of its Fourier coefficients. The description is simple and independent of the homogeneous Banach space. Saturation of such operators is also considered.