Spectral sets and the Drazin inverse with applications to second order differential equations

Trung Dinh Tran

Applications of Mathematics (2002)

  • Volume: 47, Issue: 1, page 1-8
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Tran, Trung Dinh. "Spectral sets and the Drazin inverse with applications to second order differential equations." Applications of Mathematics 47.1 (2002): 1-8. <http://eudml.org/doc/33099>.

@article{Tran2002,
abstract = {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.},
author = {Tran, Trung Dinh},
journal = {Applications of Mathematics},
keywords = {Banach space; closed linear operators; Drazin inverse; spectral sets; second order differential equations; Banach space; closed linear operator; Drazin inverse; spectral sets; second order differential equation},
language = {eng},
number = {1},
pages = {1-8},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Spectral sets and the Drazin inverse with applications to second order differential equations},
url = {http://eudml.org/doc/33099},
volume = {47},
year = {2002},
}

TY - JOUR
AU - Tran, Trung Dinh
TI - Spectral sets and the Drazin inverse with applications to second order differential equations
JO - Applications of Mathematics
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 1
SP - 1
EP - 8
AB - 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.
LA - eng
KW - Banach space; closed linear operators; Drazin inverse; spectral sets; second order differential equations; Banach space; closed linear operator; Drazin inverse; spectral sets; second order differential equation
UR - http://eudml.org/doc/33099
ER -

References

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  2. 10.2307/2308576, Amer. Math. Monthly 65 (1958), 506–514. (1958) MR0098762DOI10.2307/2308576
  3. Spectral projections, Irish Math.  Soc. Bull. 11 (1984), 10–15. (1984) Zbl0556.47001MR0762003
  4. 10.1017/S0017089500031803, Glasgow Math. J. 38 (1996), 367–381. (1996) Zbl0897.47002MR1417366DOI10.1017/S0017089500031803
  5. Spectral sets II, Rend. Circ. Mat. Palermo (Series II) 47 (1998), 293–310. (1998) MR1633491
  6. The Drazin inverse for closed linear operators, (to appear). (to appear) 
  7. Linear Differential Equations in Banach Space, Amer. Math. Soc., Providence, 1971. (1971) MR0342804
  8. The Drazin inverse for singular evolution equations and partial differential operators, World Sci. Ser. Appl. Anal. 1 (1992), 441–456. (1992) MR1180129
  9. Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin, 1983. (1983) Zbl0516.47023MR0710486
  10. Introduction to Functional Analysis, 2nd edition, Wiley, New York, 1980. (1980) MR0564653

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