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Results tagged with operator-theory
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user 230017
Spectrum, resolvent, numerical range, functional calculus, operator semigroups. Special classes of operators: compact, Fredholm, dissipative, differential, integral, pseudodifferential, etc.
3
votes
0
answers
197
views
On the spectrum of Fokker–Planck with linear drift
The paper by Liberzon and Brockett, "Spectral analysis of Fokker–Planck and related operators arising from linear stochastic differential equations." SIAM Journal on Control and Optimization 38.5 (2 …
- 116
2
votes
1
answer
152
views
Intuition/references for understanding bound states/discrete spectrum relationship
I am trying to form intuition for the following `well-known' facts about spectrum of unbounded operators (Schrodinger/wave etc.) $L$ on $\mathbb{R}^n$.
Let $\lambda\in\mathbb{R}$ satisfy
$Lf=\lambda f …
- 116
2
votes
2
answers
389
views
Does this operator have a continuous, localized eigenfunction with negative eigenvalue?
I am looking at a class of operators
$$
L[f](x)=af_{xxxx}-bf_{xx}+\frac{d}{dx}(\delta(x)f_x)
$$ , a<0,b<0,
on the real line, where $\delta$ is Dirac-delta.
I am interested in ruling out the possibilit …
- 116