Publication Cover
Applicable Analysis
An International Journal
Volume 80, 2001 - Issue 1-2
47
Views
17
CrossRef citations to date
0
Altmetric
Original Articles

Riesz basis of root vectors of a non-symmetric system of first-order ordinary differential operators and application to inverse eigenvalue problems

&
Pages 19-51 | Received 20 Feb 2001, Published online: 02 May 2007

  • Borg , G. 1946 . Eine Umkehrung der Sturm-Liouvilleschen Eigenwerfrage . Acta Math. , 78 : 1 – 96 .
  • Cox , S. and Knobel , R. 1996 . An inverse spectral problem for a nonnormal first order differential operator . Integr. Equat. Oper. Th. , 25 : 147 – 162 .
  • Cox , S. and Knobel , R. 1994 . The rate at which energy decays ina damping string . Commun. in Partial Differential Equations , 19 : 213 – 243 .
  • Gladwell , G.M.L. 1986 . Inverse Problems in Vibrations , Dordrecht : Kluwer .
  • Gohberg , I.C. and Krein , M.G. 1969 . Introduction to the Theory of Linear Nonselfadjoint Operators , Providence, Rhode Island : American Mathematical Society .
  • Gomilko , A. and Pivovarchik , V. 1999 . On bases of eigenfunctions of boundary problem associated with small vibrations of damped nonsmooth inhomogeneous string . Asympt. Analysis , 20 : 301 – 315 .
  • Hald , O. 1984 . Discontinuous inverse eigenvalue problems . Comm. Pure Appl. Math. , 37 : 539 – 577 .
  • Hochstadt , H. 1973 . The inverse Sturm-Liouville problem . Comm. Pure Appl. Math. , 26 : 715 – 729 .
  • Hochstadt , H. 1975 . On inverse problems associated with Sturm-Liouville operators . J. Differential Equations , 17 : 220 – 235 .
  • Johnson , W.C. 1950 . Transmission Lines and Networks , Newyork : McGraw-Hill .
  • Kato , T. 1980 . Perturbation Theory for Linear Operators , Berlin : Springer Verlag .
  • Levinson , N. 1949 . The inverse Sturm-Liouville problem . Mat. Tidsskr. B , 1949 : 25 – 30 .
  • Levitan , B.M. 1987 . Inverse Sturm-Liouville Problems , Zeist : VSP .
  • Levitan , B.M. and Gasymov , M.G. 1964 . Determination of a differential equation by two of its spectra . Russian Mathematical Surveys , 19 ( 2 ) : 1 – 63 .
  • Levitan , B.M. and Sargsjan , I.S. 1991 . Sturm-Liouville and Dirac Operators , Dordrecht : Kluwer .
  • Marchenko , V.A. 1950 . On certain questions in the theory of differential operators of second order . Dokl. Akad. Nauk SSSR , 72 : 457 – 460 .
  • Marchenko , V.A. 1986 . Sturm-Liouville Operators and Applications , Basel : Birkhäuser-Verlag .
  • Pivovarchik , V. 1997 . Inverse problem for a smooth string with damping at one end . J. Operator Therory , 38 : 243 – 263 .
  • Pivovarchik , V. 1999 . Direct and inverse problems for a damped string . J. Operator Therory , 38 : 189 – 220 .
  • Pöschel , J. and Trubowitz , E. 1987 . Inverse Spectral Theory , Orlando, Florida : Academic Press .
  • Russell , D.L. 1972 . Control theory of hyperbolic equations related to certain questions in harmonic analysis and spectral theory . J. Math. Anal. Appl. , 40 : 336 – 368 .
  • Russell , D.L. 1978 . Canonical forms and spectral determination for a class of hyperbolic distributed parameter control systems . J. Math. Anal. Appl. , 62 : 186 – 225 .
  • Rykhlov , V.S. 1992 . On completeness of eigenfunctions of quardratic bundles of ordinary differential operators . Russian Mathematics (Iz. VUZ) , 36 ( 3 ) : 33 – 42 .
  • Shkalikov , A.A. 1983 . “ Boundary vale problems for ordianary diffrential equation with parameter in the boundary conditions ” . In Trudy semin. im. I.G. Petrovskogo , Vol. 9 , 190 – 229 . Moscow : Izd-vo Mosk. Univ. .
  • Shubov , M.A. 1997 . Spectral operators generated by damped hyperbolic equations . Integr. Equat. Oper. Th. , 28 : 358 – 372 .
  • Shubov , M.A. 2000 . Riesz basis property of root vectors of nonselfadjoint operators generated by radial damped wave equations . Adv. Differ. Equat. , 5 ( 4–6 ) : 623 – 656 .
  • Shubov , M.A. , Martin , C.F. , Dauer , J.P. and Belinskiy , B.P. 1997 . Exact controllability of the damped wave equation . SIAM J. Control Optim , 35 ( 4–6 ) : 1773 – 1789 .
  • Suzuki , T. 1985 . Gel'fand-Levitan' theory, deformation formulas and inverse problems . Journal of the Faculty of Science, The University of Tokyo, Sec. IA, Math. , 32 ( 4–6 ) : 223 – 271 .
  • Vagabov , A.I. 1987 . Quadratic bundles of ordinary differential bundles . Math. Zametki , 42 ( 4–6 ) : 708 – 715 .
  • Yamamoto , M. 1988 . Inverse spectral problem for systems of ordianary differential equations of first order, I . Journal of the Faculty of Science, The University of Tokyo, Sec. IA, Math. , 35 ( 4–6 ) : 519 – 546 .
  • Yamamoto , M. 1990 . Inverse eigenvalue problem for a vibration of a string with viscous drag . J. Math. Anal. Appl. , 152 ( 4–6 ) : 20 – 34 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.