- 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 .
Riesz basis of root vectors of a non-symmetric system of first-order ordinary differential operators and application to inverse eigenvalue problems
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.
Related research
People also read lists articles that other readers of this article have read.
Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.
Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.