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Putnam
1948 Putnam
B4
Putnam 1948 B4
Putnam 1948 B4
Source: Putnam 1948
March 15, 2022
Putnam
functional equation
integration
Problem Statement
For what
λ
\lambda
λ
does the equation
∫
0
1
min
(
x
,
y
)
f
(
y
)
d
y
=
λ
f
(
x
)
\int_{0}^{1} \min(x,y) f(y)\; dy =\lambda f(x)
∫
0
1
min
(
x
,
y
)
f
(
y
)
d
y
=
λ
f
(
x
)
have continuous solutions which do not vanish identically in
(
0
,
1
)
?
(0,1)?
(
0
,
1
)?
What are these solutions?
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