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Miklós Schweitzer
1956 Miklós Schweitzer
9
9
Part of
1956 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1956- Problem 9
Source:
10/11/2015
9. Show that if the trigonometric polynomial
f
(
θ
)
=
∑
v
=
1
n
a
v
cos
v
θ
f(\theta)= \sum_{v=1}^{n} a_v \cos v\theta
f
(
θ
)
=
∑
v
=
1
n
a
v
cos
v
θ
monotonically decreases over the closed interval
[
0
,
π
]
[0,\pi]
[
0
,
π
]
, then the trigonometric polynomial
g
(
θ
)
=
∑
v
=
1
n
a
v
sin
v
θ
g(\theta)=\sum_{v=1}^{n}a_v \sin v\theta
g
(
θ
)
=
∑
v
=
1
n
a
v
sin
v
θ
is non negative in the same interval. (S. 26)
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