Methods of approximation theory in research of harmonic analysis and wavelets
Shi Xian-liang, Chen Yang · Scientia Sinica Mathematica · 2018
In this paper, we give a brief introduction about applications of approxiamtion theory of functions in harmonic analysis and wavelet research.We start from Korovkin's theorem to introduce applications of test functions in wavelet research. Then we present boundedness of singular integrals by using Jackson approximation.In addition, applications of regular linear summation and approximation in edge detection and inverse Fourier transform are stated. We also introduce some new results in signal reconstruction by sparse data.