MathDB

Fourier series convergent/divergent simultaneously

Source: 2021 Miklos Schweitzer, P6

November 2, 2021

real analysisfourier analysis

Problem Statement

Let

f

and

g

2 \pi

-periodic integrable functions such that in some neighborhood of

0

g(x) = f(ax)

with some

a \neq 0

. Prove that the Fourier series of

f

and

g

are simultaneously convergent or divergent at

0