| Title:
|
Spectral sets and the Drazin inverse with applications to second order differential equations (English) |
| Author:
|
Tran, Trung Dinh |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
1-8 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper defines and studies the Drazin inverse for a closed linear operator $A$ in a Banach space $X$ in the case that $0$ belongs to a spectral set of the spectrum of $A$. Results are applied to extend a result of Krein on a nonhomogeneous second order differential equation in a Banach space. (English) |
| Keyword:
|
Banach space |
| Keyword:
|
closed linear operators |
| Keyword:
|
Drazin inverse |
| Keyword:
|
spectral sets |
| Keyword:
|
second order differential equations |
| MSC:
|
34G10 |
| MSC:
|
47A05 |
| MSC:
|
47A10 |
| MSC:
|
47A60 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1068.47005 |
| idMR:
|
MR1876488 |
| DOI:
|
10.1023/A:1021793115985 |
| . |
| Date available:
|
2009-09-22T18:08:21Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134481 |
| . |
| Reference:
|
[1] S. L. Campbell: Singular Systems of Differential Equations. Research Notes in Mathematics 40.Pitman, London, 1980. MR 0569589 |
| Reference:
|
[2] M. P. Drazin: Pseudo-inverse in associative rings and semigroups.Amer. Math. Monthly 65 (1958), 506–514. MR 0098762, 10.2307/2308576 |
| Reference:
|
[3] R. E. Harte: Spectral projections.Irish Math. Soc. Bull. 11 (1984), 10–15. Zbl 0556.47001, MR 0762003 |
| Reference:
|
[4] J. J. Koliha: A generalized Drazin inverse.Glasgow Math. J. 38 (1996), 367–381. Zbl 0897.47002, MR 1417366, 10.1017/S0017089500031803 |
| Reference:
|
[5] J. J. Koliha, Pak Wai Poon: Spectral sets II.Rend. Circ. Mat. Palermo (Series II) 47 (1998), 293–310. MR 1633491 |
| Reference:
|
[6] J. J. Koliha, Trung Dinh Tran: The Drazin inverse for closed linear operators.(to appear). |
| Reference:
|
[7] S. G. Krein: Linear Differential Equations in Banach Space.Amer. Math. Soc., Providence, 1971. MR 0342804 |
| Reference:
|
[8] M. Z. Nashed, Y. Zhao: The Drazin inverse for singular evolution equations and partial differential operators.World Sci. Ser. Appl. Anal. 1 (1992), 441–456. MR 1180129 |
| Reference:
|
[9] A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations.Springer-Verlag, Berlin, 1983. Zbl 0516.47023, MR 0710486 |
| Reference:
|
[10] A. E. Taylor, D. C. Lay: Introduction to Functional Analysis, 2nd edition.Wiley, New York, 1980. MR 0564653 |
| . |
