| Title:
|
Two separation criteria for second order ordinary or partial differential operators (English) |
| Author:
|
Brown, R. C. |
| Author:
|
Hinton, D. B. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
124 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
273-292 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We generalize a well-known separation condition of Everitt and Giertz to a class of weighted symmetric partial differential operators defined on domains in $\Bbb R^n$. Also, for symmetric second-order ordinary differential operators we show that $\limsup_{t\to c} (pq')'/q^2=\theta<2$ where $c$ is a singular point guarantees separation of $-(py')'+qy$ on its minimal domain and extend this criterion to the partial differential setting. As a particular example it is shown that $-\Delta y+qy$ is separated on its minimal domain if $q$ is superharmonic. For $n=1$ the criterion is used to give examples of a separation inequality holding on the domain of the minimal operator in the limit-circle case. (English) |
| Keyword:
|
separation |
| Keyword:
|
ordinary or partial differential operator |
| Keyword:
|
limit-point |
| Keyword:
|
essentially selfadjoint |
| MSC:
|
26D10 |
| MSC:
|
34B05 |
| MSC:
|
34C05 |
| MSC:
|
34L05 |
| MSC:
|
34L40 |
| MSC:
|
35B45 |
| MSC:
|
35P05 |
| MSC:
|
47E05 |
| MSC:
|
47F05 |
| idZBL:
|
Zbl 0937.34068 |
| idMR:
|
MR1780697 |
| DOI:
|
10.21136/MB.1999.126251 |
| . |
| Date available:
|
2009-09-24T21:37:59Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126251 |
| . |
| Reference:
|
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