Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
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 L2(a,b) and the infinitesimal generator of a C0-semigroup of bounded linear operators.
Rocznik
Tom
Strony
481--484
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- CESAME, Université Catholique de Louvain, 4, Avenue G. Lemaître, B–1348 Louvain-la-Neuve, Belgium
autor
- CESAME, Université Catholique de Louvain, 4, Avenue G. Lemaître, B–1348 Louvain-la-Neuve, Belgium
autor
- Department of Mathematics, University of Namur (FUNDP), 8, Rempart de la Vierge, B–5000 Namur, Belgium
Bibliografia
- [1] 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.
- [2] Birkhoff G. (1962): Ordinary Differential Equations.—Boston: Ginn.
- [3] Curtain R.F. and Zwart H. (1995): An Introduction to Infinite-Dimensional Linear Systems Theory. — New York: Springer.
- [4] 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.
- [5] Laabissi M., Achhab M.E., Winkin J. and Dochain D. (2001): Trajectory analysis of a nonisothermal tubular reactor nonlinear models. — Syst. Contr. Lett., Vol. 42, No. 3, pp. 169–184.
- [6] Naylor A.W. and Sell G.R. (1982): Linear Operator Theory in Engineering and Science.—New York: Springer.
- [7] Pazy A. (1983): Semigroups of Linear Operators and Applications to Partial Differential Equations. — New York: Springer.
- [8] Pryce J.D. (1993): Numerical Solutions of Sturm-Liouville Problems.— New York: Oxford University Press.
- [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.
- [11] Sagan H. (1961): Boundary and Eigenvalue Problems in Mathematical Physics.—New York: Wiley.
- [12] Winkin J., Dochain D. and Ligarius Ph. (2000): Dynamical analysis of distributed parameter tubular reactors. — Automatica, Vol. 36, No. 3, pp. 349–361.
- [13] Young E.C. (1972): Partial Differential Equations: An Introduction.— Boston: Allyn and Bacon.
- [14] Young R.M. (1980): An Introduction to Nonharmonic Fourier Series.—New York: Academic Press.
- [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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0002-0042