# 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

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topDelattre, 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

top- Belinskiy B.P. and Dauer J.P. (1997): On regular Sturm-Liouville problem on a finite interval with the eigenvalue parameter appearing linearly in the boundary conditions, In: Spectral Theory and Computational Methods of Sturm-Liouville Problems (D. Hinton and P.W. Schaefer, Eds.). -New York: Marcel Dekker, pp. 183-196. Zbl0879.34035
- Birkhoff G. (1962): Ordinary Differential Equations.- Boston: Ginn. Zbl0102.29901
- Curtain R.F. and Zwart H. (1995): An Introduction to Infinite-Dimensional Linear Systems Theory.- New York: Springer. Zbl0839.93001
- Kuiper C.R. and Zwart H.J. (1993): Solutions of the ARE in terms of the Hamiltonian for Riesz-spectral systems. - Lect. Not. Contr. Inf. Sci., Vol. 185, pp. 314-325. Zbl0793.93066
- 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
- Naylor A.W. and Sell G.R. (1982): Linear Operator Theory in Engineering and Science.- New York: Springer. Zbl0497.47001
- Pazy A. (1983): Semigroups of Linear Operators and Applications to Partial Differential Equations. - New York: Springer. Zbl0516.47023
- Pryce J.D. (1993): Numerical Solutions of Sturm-Liouville Problems.- New York: Oxford University Press. Zbl0795.65053
- Ray W.H. (1981): Advanced Process Control. -Boston: Butterworths.
- Renardy M. and Rogers R.C. (1993): An Introduction to Partial Differential Equations. - New York: Springer. Zbl0917.35001
- Sagan H. (1961): Boundary and Eigenvalue Problems in Mathematical Physics.- New York: Wiley. Zbl0106.37303
- 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
- Young E.C. (1972): Partial Differential Equations: An Introduction.- Boston: Allyn and Bacon. Zbl0228.35001
- Young R.M. (1980): An Introduction to Nonharmonic Fourier Series.- New York: Academic Press. Zbl0493.42001
- 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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