Sturm-Liouville systems are Riesz-spectral systems

• Autorzy: Cédric Delattre , Denis Dochain , Joseph Winkin
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

C_0-semigroup; Riesz-spectral system; Sturm-Liouville system; infinite-dimensional state-space system

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2003
• Tom: 13
• Numer: 4
• Strony: 481-484

Daty

wydano

2003

otrzymano

2003-01-15

poprawiono

2003-05-21

(nieznana)

2003-07-13

Twórcy

autor

Cédric Delattre

• CESAME, Université Catholique de Louvain, 4, Avenue G. Lemaître, B-1348 Louvain-la-Neuve, Belgium

autor

Denis Dochain

• CESAME, Université Catholique de Louvain, 4, Avenue G. Lemaître, B-1348 Louvain-la-Neuve, Belgium

autor

Joseph Winkin

• Department of Mathematics, University of Namur (FUNDP), 8, Rempart de la Vierge, B-5000 Namur, Belgium

Bibliografia

• 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.
• Birkhoff G. (1962): Ordinary Differential Equations.- Boston: Ginn.
• Curtain R.F. and Zwart H. (1995): An Introduction to Infinite-Dimensional Linear Systems Theory.- New York: Springer.
• 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.
• 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.
• Naylor A.W. and Sell G.R. (1982): Linear Operator Theory in Engineering and Science.- New York: Springer.
• Pazy A. (1983): Semigroups of Linear Operators and Applications to Partial Differential Equations. - New York: Springer.
• Pryce J.D. (1993): Numerical Solutions of Sturm-Liouville Problems.- New York: Oxford University Press.
• 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.
• Sagan H. (1961): Boundary and Eigenvalue Problems in Mathematical Physics.- New York: Wiley.
• Winkin J., Dochain D. and Ligarius Ph. (2000): Dynamical analysis of distributed parameter tubular reactors. - Automatica, Vol. 36, No. 3, pp. 349-361.
• Young E.C. (1972): Partial Differential Equations: An Introduction.- Boston: Allyn and Bacon.
• Young R.M. (1980): An Introduction to Nonharmonic Fourier Series.- New York: Academic Press.
• 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.