MathDB
Problems
Contests
Undergraduate contests
Miklós Schweitzer
2021 Miklós Schweitzer
6
6
Part of
2021 Miklós Schweitzer
Problems
(1)
Fourier series convergent/divergent simultaneously
Source: 2021 Miklos Schweitzer, P6
11/2/2021
Let
f
f
f
and
g
g
g
be
2
π
2 \pi
2
π
-periodic integrable functions such that in some neighborhood of
0
0
0
,
g
(
x
)
=
f
(
a
x
)
g(x) = f(ax)
g
(
x
)
=
f
(
a
x
)
with some
a
≠
0
a \neq 0
a
=
0
. Prove that the Fourier series of
f
f
f
and
g
g
g
are simultaneously convergent or divergent at
0
0
0
.
real analysis
fourier analysis