Sturm-Liouville systems are Riesz-spectral systems

Cédric Delattre; Denis Dochain; Joseph Winkin

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 4, page 481-484
  • ISSN: 1641-876X

Abstract

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The class of Sturm-Liouville systems is defined. It appears to be a subclass of Riesz-spectral systems, since it is shown that the negative of a Sturm-Liouville operator is a Riesz-spectral operator on L^2(a,b) and the infinitesimal generator of a C_0-semigroup of bounded linear operators.

How to cite

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Delattre, Cédric, Dochain, Denis, and Winkin, Joseph. "Sturm-Liouville systems are Riesz-spectral systems." International Journal of Applied Mathematics and Computer Science 13.4 (2003): 481-484. <http://eudml.org/doc/207659>.

@article{Delattre2003,
abstract = {The class of Sturm-Liouville systems is defined. It appears to be a subclass of Riesz-spectral systems, since it is shown that the negative of a Sturm-Liouville operator is a Riesz-spectral operator on L^2(a,b) and the infinitesimal generator of a C\_0-semigroup of bounded linear operators.},
author = {Delattre, Cédric, Dochain, Denis, Winkin, Joseph},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {C\_0-semigroup; Riesz-spectral system; Sturm-Liouville system; infinite-dimensional state-space system; Sturm-Liouville operator; infinite-dimensional systems; Riesz spectral system; strongly continuous semigroup},
language = {eng},
number = {4},
pages = {481-484},
title = {Sturm-Liouville systems are Riesz-spectral systems},
url = {http://eudml.org/doc/207659},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Delattre, Cédric
AU - Dochain, Denis
AU - Winkin, Joseph
TI - Sturm-Liouville systems are Riesz-spectral systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 4
SP - 481
EP - 484
AB - The class of Sturm-Liouville systems is defined. It appears to be a subclass of Riesz-spectral systems, since it is shown that the negative of a Sturm-Liouville operator is a Riesz-spectral operator on L^2(a,b) and the infinitesimal generator of a C_0-semigroup of bounded linear operators.
LA - eng
KW - C_0-semigroup; Riesz-spectral system; Sturm-Liouville system; infinite-dimensional state-space system; Sturm-Liouville operator; infinite-dimensional systems; Riesz spectral system; strongly continuous semigroup
UR - http://eudml.org/doc/207659
ER -

References

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  5. Laabissi M., Achhab M.E., Winkin J. and Dochain D. (2001): Trajectory analysis of a nonisothermal tubular reactor nonlinearmodels. - Syst. Contr. Lett., Vol. 42, No. 3, pp. 169-184. Zbl0985.93030
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  7. Pazy A. (1983): Semigroups of Linear Operators and Applications to Partial Differential Equations. - New York: Springer. Zbl0516.47023
  8. Pryce J.D. (1993): Numerical Solutions of Sturm-Liouville Problems.- New York: Oxford University Press. Zbl0795.65053
  9. Ray W.H. (1981): Advanced Process Control. -Boston: Butterworths. 
  10. Renardy M. and Rogers R.C. (1993): An Introduction to Partial Differential Equations. - New York: Springer. Zbl0917.35001
  11. Sagan H. (1961): Boundary and Eigenvalue Problems in Mathematical Physics.- New York: Wiley. Zbl0106.37303
  12. Winkin J., Dochain D. and Ligarius Ph. (2000): Dynamical analysis of distributed parameter tubular reactors. - Automatica, Vol. 36, No. 3, pp. 349-361. Zbl0979.93077
  13. Young E.C. (1972): Partial Differential Equations: An Introduction.- Boston: Allyn and Bacon. Zbl0228.35001
  14. Young R.M. (1980): An Introduction to Nonharmonic Fourier Series.- New York: Academic Press. Zbl0493.42001
  15. Zhidkov P.E. (2000): Riesz basis property of the system of eigenfunctions for a non-linear problem of Sturm-Liouville type.- Sbornik Mathematics, Vol. 191, Nos. 3-4, pp. 359-368. Zbl0961.34072

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