\(J\)-selfadjoint ordinary differential operators similar to selfadjoint operators (Q2711780)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: \(J\)-selfadjoint ordinary differential operators similar to selfadjoint operators |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(J\)-selfadjoint ordinary differential operators similar to selfadjoint operators |
scientific article |
Statements
25 April 2001
0 references
\(J\)-selfadjoint operator
0 references
similarity
0 references
0.9714644
0 references
0.9305282
0 references
0.92997223
0 references
0.9106314
0 references
0.91034687
0 references
0.90254647
0 references
0 references
\(J\)-selfadjoint ordinary differential operators similar to selfadjoint operators (English)
0 references
Let \(p(t)\) be an even order polynomial with real coefficients. The operator \(A=(\text{sgn} t)p(-i\frac{d}{dt})\) on \(L_2(\mathbb R)\) is \(J\)-self adjoint if \(J\) is the operator of multiplication by \(\text{sgn} t\). It is shown that \(A\) is similar to a selfadjoint operator if and only if the polynomial \(p\) is non-negative.
0 references
