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2003 | 13 | 4 | 481-484
Tytuł artykułu

Sturm-Liouville systems are Riesz-spectral systems

Treść / Zawartość
Warianty tytułu
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.
Rocznik
Tom
13
Numer
4
Strony
481-484
Opis fizyczny
Daty
wydano
2003
otrzymano
2003-01-15
poprawiono
2003-05-21
(nieznana)
2003-07-13
Twórcy
  • CESAME, Université Catholique de Louvain, 4, Avenue G. Lemaître, B-1348 Louvain-la-Neuve, Belgium
  • CESAME, Université Catholique de Louvain, 4, Avenue G. Lemaître, B-1348 Louvain-la-Neuve, Belgium
  • 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.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv13i4p481bwm
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