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Results tagged with operator-theory
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user 113514
Spectrum, resolvent, numerical range, functional calculus, operator semigroups. Special classes of operators: compact, Fredholm, dissipative, differential, integral, pseudodifferential, etc.
2
votes
2
answers
279
views
Domain of Schrödinger operators
Let $S$ be a Schrödinger operator on $\mathbb{R}$, $Su=-u''+Vu$ with $V\geq1$ continuous and going to $+\infty$ at infinity (you can think of it as $x^2+1$). I wondering which assumptions do I have to …
- 41
0
votes
1
answer
133
views
When integrating by part produces a singularity
I'm currently interesting in the following operator:
$$O[f](x):=f(x)-2xe^{x^2}\int_x^{+\infty}dt \, e^{-t^2} f(t)$$ for all $x\in\mathbb{R}$ and $f$ smooth and decaying at infinity fast enough with th …
- 41
1
vote
0
answers
21
views
Regularity of solutions of a 2nd order singular integro-differential operator
I have trouble finding the regularity of the solutions to a particular equation. I define
$$\mathcal{L}f(x)=f''(x)+x^2f'(x)+ \operatorname{p.\!v.\!\!}\int_{-\infty}^{+\infty} \dfrac{f'(t)e^{-t^2}}{t-x …
- 41
1
vote
0
answers
119
views
Continuity of a minimizing measure w.r.t a parameter
Let $V_t(x)=x^2+t\phi(x)$ where $t>0$ and $\phi\in C^\infty_c(\mathbb{R})$.
My question is what can be said about the continuity of the (unique) minimizer (among probability measures) of the following …
- 41