Basis Properties and Completeness of Certain System of Elementary Functions by E. I. Moiseev

The possibility of approximating functions of a sufficiently general form by relatively simple functions and therefore more convenient for analysis and computation is the initial reason for approximation theory. The basic fact of this theory is the Weierstrasse theorem. In the first part of this book the authors consider the problem of description of complete power systems. In the second part, the authors study the problem on bases in Sobolev spaces, in their subspaces and also in weighted spaces and finally consider continuous analogs of basis expansions (the generalized sine and cosine Fourier transforms).

Cambridge Scientific Publishers