Questions tagged [self-adjoint-operators]
478 questions
2
votes
2 answers
Why is the second derivative operator self-adjoint?
I read that a second derivative operator is self-adjoint, namely $\langle L(u),v\rangle=\langle u,L(v)\rangle$ and $L$ is the second derivative operator.
But if I define $$\langle u,v\rangle=\int_0^1 u(x)v(x)\text{d}x,$$ I just don't see how it…
Tomer
- 434
0
votes
0 answers
Sum of the eigenspaces of a non compact self-adjoint bounded operator
Let $\mathcal H$ be a separable Hilbert space, and $\mathbf A: \mathcal H\rightarrow\mathcal H$ a bounded self-adjoint yet non-compact operator.
Suppose that I can construct a sequence $(\mathbf A_n)_{n\geq 0}$ of compact self-adjoint operators over…
Cyril Soler
- 75
0
votes
0 answers
Self-adjoint operator in $L^2(\mathbb Q_p)$.
Let $g:\mathbb Q_p^n\longrightarrow{\mathbb Z}$ increasing and radial. We define the following operator
$$Hf(x)=\frac{1}{p^{n\left|{g(x)}\right|}}\displaystyle\int_{B_{g(x)}^n}\left |{f(y)}\right |dy$$
where $p$ is a fixed prime number and…
Luis De Oro
- 27
0
votes
0 answers
disconjugacy of a self adjoint operator
How we can cheek if this defference equation $-\Delta^2 y(t)=0$ is disconjugate or not?
We have this definition:
We say that the difference equation $\Delta (p(t-1)\Delta y(t-1))+q(t)y(t)=0$ is "disconjugate" on $[a, b+
2]=\{a, a+1,...,b+2\}$…
L_Green
- 23
0
votes
0 answers
Spectrum of bounded self adjoint operator
Let $A$ be bounded self adjoint operator. Then, at least one or both of $\|A\|$, $-\|A\|$ is in spectrum $\sigma(A)$. I can not prove this.
I'd appreciate it if you could help.
sate
- 195