| Title:
|
Generalized communication conditions and the eigenvalue problem for a monotone and homogenous function
(English)
|
| Author:
|
Cavazos-Cadena, Rolando |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
46 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
665-683 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This work is concerned with the eigenvalue problem for a monotone and homogenous self-mapping $f$ of a finite dimensional positive cone. Paralleling the classical analysis of the (linear) Perron–Frobenius theorem, a verifiable communication condition is formulated in terms of the successive compositions of $f$, and under such a condition it is shown that the upper eigenspaces of $f$ are bounded in the projective sense, a property that yields the existence of a nonlinear eigenvalue as well as the projective boundedness of the corresponding eigenspace. The relation of the communication property studied in this note with the idea of indecomposability is briefly discussed. |
| Keyword:
|
projectively bounded and invariant sets |
| Keyword:
|
generalized Perron–Frobenius conditions |
| Keyword:
|
nonlinear eigenvalue |
| Keyword:
|
Collatz–Wielandt relations |
| MSC:
|
47H07 |
| MSC:
|
47H09 |
| MSC:
|
47J10 |
| idZBL:
|
Zbl 1208.47059 |
| idMR:
|
MR2722094 |
| . |
| Date available:
|
2010-10-22T05:25:38Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140777 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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