Search

In this paper, we prove a new uncertainty principle for functions with radial symmetry by differentiating a radial version of the Stein–Weiss inequality. The difficulty is to prove the differentiability in the limit of the best constant that unlike the general case it is not known. We provide also an integral alternative formula for the logarithmic weight $(\log|\xi|)$ in Fourier domain.

Summary

This chapter is a close companion to the previous one. Here we study the best least squares approximation to periodic functions via trigonometric polynomials. Many of the ideas and results of the previous chapter are repeated in this scenario. They are then expanded to deal with merely square integrable functions. The Fourier transform of periodic functions, and its inverse, is then introduced and studied. Uniform convergence of trigonometric series, under several different smoothness assumptions is then discussed.Trigonometric approximation in periodic Sobolev spaces is then discussed.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

A logarithmic uncertainty principle for functions with radial symmetry

12 - Fourier Series

Summary

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

A logarithmic uncertainty principle for functions with radial symmetry

12 - Fourier Series

Summary