# On the Fourier transform of a function of several variables

Mon, 28/03/2016 - 14:00

Speaker:

Prof. R. Trigub

Seminar:

Place:

2nd floor Colloquium Room, Building 216

Abstract:

For functions $f(x_{1},x_{2})=f_{0}\big(\max\{|x_{1}|,|x_{2}|\}\big)$ from

$L_{1}(\mathbb{R}^{2})$, sufficient and necessary conditions for the belonging of their Fourier transform

$\widehat{f}$ to $L_{1}(\mathbb{R}^{2})$ as well as of a function $t\cdot \sup\limits_{y_{1}^{2}+y_{2}^{2}\geq

t^{2}}\big|\widehat{f}(y_{1},y_{2})\big|$ to $L_{1}(\mathbb{R}^{1}_{+})$. As for the positivity of $\widehat{f}$ on

$\mathbb{R}^{2}$, it is completely reduced to the same question on $\mathbb{R}^{1}$ for a function

$f_{1}(x)=|x|f_{0}\big(|x|\big)+\int\limits_{|x|}^{\infty}f_{0}(t)dt$.

- Last modified: 21/03/2016