Tagged Questions
3
votes
0answers
111 views
show that the function satisfies condition of the lemma
Let $(f_n)_{n\geq 0}$ be an eigenfunctions of the compact integral operator
$F$, defined on $L^2([-1,1])$ by
$$
F(f)(x)=\int_{-1}^1\frac{\sin a(x-y)}{x-y}\,\psi(y)\,\mathrm{d}y, \quad \mbox{here ...
2
votes
0answers
191 views
Homogeneous Fredholm Equation of Second Kind
I'm trying to show that the eigenvalues of the following integral equation
\begin{align*}
\lambda \phi(t) = \int_{-T/2}^{T/2} dx \phi(x)e^{-\Gamma|t-x|}
\end{align*}
are given by
\begin{align*}
...
0
votes
1answer
167 views
Linear versus non-linear integral equations
I'm having trouble solving an integral equation. It appears to me to be a homogeneous Fredholm equation of the second kind. However, I'm being told that this can't be a Fredholm equation, because it ...
2
votes
1answer
403 views
Eigenvalues of an operator
I think this question isn't that hard, but I am a bit confused:
Define $$(Af)(x):=\int_{0}^{1}\cos(2\pi(x-y))f(y)dy.$$ Then $A$ is an operator on functions. Find the eigenvalues and the ...
