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4 votes
1 answer
286 views

Eigenvalue of a convolution and a restriction?

Let $\epsilon>0$ be small. Let $\eta(t) = \frac{2\epsilon}{\epsilon^2+(2\pi t)^2}$ (the Fourier transform of $x\mapsto e^{-\epsilon |x|}$). Let $V$ be the space of integrable, bounded functions $f:\...
H A Helfgott's user avatar
  • 20.2k
1 vote
1 answer
195 views

Eigenvalues of operator

In the question here the author asks for the eigenvalues of an operator $$A = \begin{pmatrix} x & -\partial_x \\ \partial_x & -x \end{pmatrix}.$$ Here I would like to ask if one can extend ...
Kung Yao's user avatar
  • 192
6 votes
0 answers
107 views

Eigenvalues of splitting scheme

In numerical analysis it is common to approximate a solution to a PDE $$u'(t) = (A+B) u(t), \quad u(0)=u_0$$ which is just given by $e^{t(A+B)}u_0$ by the splitting $e^{tB/2} e^{tA} e^{tB/2}u_0.$ Here,...
Sascha's user avatar
  • 536
2 votes
1 answer
134 views

Common eigenvalues for two Sturm-Liouville problem

Does exist in literature any results concerning the common eigenvalues for the two eigenvalue problems of the form $$y''(x)=\lambda^2 y(x)+\lambda a(x)y(x), \ x\in(0,1), $$$$z''(x)=\lambda^2 z(x)-\...
Gustave's user avatar
  • 617
2 votes
0 answers
463 views

Conditions for continuity of non-simple eigenvectors

Here, https://math.stackexchange.com/a/1146455, it is noted that eigenprojections are continuous, but eigenvectors are not. Are there any conditions where the eigenvalues are not simple, but the ...
billbob's user avatar
  • 37
0 votes
0 answers
244 views

Checking whether this would be bounded

It may be better to post this question here. Assume that $M$ is an $m$ by $m$ ($m$ is an even number) symmetric positive-semi-definite matrix with exactly $m/2$ positive eigenvalues and every entry of ...
io0's user avatar
  • 1