| Title:
|
Derivative of the norm of a linear mapping and its application to differential equations (English) |
| Author:
|
Tumajer, František |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
37 |
| Issue:
|
3 |
| Year:
|
1992 |
| Pages:
|
193-199 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper the notion of the derivative of the norm of a linear mapping in a normed vector space is introduced. The fundamental properties of the derivative of the norm are established. Using these properties, linear differential equations in a Banach space are studied and lower and upper estimates of the norms of their solutions are derived. (English) |
| Keyword:
|
derivative of the norm of a linear mapping |
| Keyword:
|
linear differential equations in a Banach space |
| Keyword:
|
normed space |
| Keyword:
|
solution of the differential equation |
| MSC:
|
34A30 |
| MSC:
|
34G10 |
| MSC:
|
47A30 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 0767.34045 |
| idMR:
|
MR1157455 |
| DOI:
|
10.21136/AM.1992.104503 |
| . |
| Date available:
|
2008-05-20T18:43:35Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104503 |
| . |
| Reference:
|
[1] A. N. Kolmogorov S. V. Fomin: Foundations of the theory of functions and functional analysis.(Russian). Czech translation, Praha, 1975. |
| Reference:
|
[2] J. Dieudonné: Foundations of modern analysis.Academic Press, New York-London, 1960; Russian translation, Mir, Moscow. MR 0120319 |
| . |
