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Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 12
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Articles

Inverse problem for a damped Stieltjes string from parts of spectra

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Pages 2605-2619 | Received 30 Sep 2014, Accepted 07 Dec 2014, Published online: 08 Jan 2015

References

  • Gantmakher FR, Krein MG. Oscillating matrices and kernels and vibrations of mechanical systems. Berlin: German Transl. Akademie Verlag; 1960. GITTL, Moscow-Leningrad, 1950. Russian.
  • Kurchanov PF, Myshkis AD, Filimonov AM. Train vibrations and Kronecker’s theorem (in Russian). Prikl. Mat. Mekh. 1991;55:989–995.
  • Filimonov AM, Kurchanov PF, Myshkis AD. Some unexpected results in the classical problem of vibrations of the string with n beads when n is large. C.R. Acad. Sci. Paris Sér. I Math. 1991;313:961–965.
  • Filimonov AF, Myshkis AD. On properties of large wave effect in classical problem of bead string vibration. J. Differ. Equ. Appl. 2004;10:1171–1175.
  • Gladwell G. Inverse problems in vibration. Dordrecht: Kluwer Academic Publishers; 2004.
  • Gladwell G. Matrix inverse eigenvalue problems. In: Gladwell G, A Morassi, editors. Dynamical inverse problems: theory and applications. Vol. 529, CISM Courses and Lectures. Vienna: Springer; 2011. p. 1–29.
  • Marchenko VA. Introduction to the theory of inverse problems of spectral analysis. Kharkov: Acta; 2005. Russian.
  • Cox SJ, Embree M, Hokanson JM. One can hear the composition of a string: experiments with an inverse eigenvalue problem. SIAM Rev. 2012;54:157–178.
  • Genin J, Maybee JS. Mechanical vibration trees. J. Math. Anal. Appl. 1974;45:746–763.
  • Pivovarchik V, Rozhenko N, Tretter C. Dirichlet–Neumann inverse spectral problem for a star graph of Stieltjes strings. Linear Algebra Appl. 2013;439:2263–2292.
  • Law C-K, Pivovarchik V, Wang W. A polynomial identity and its application to inverse spectral problems in Stieltjes strings. Oper. Matrices. 2013;7:603–616.
  • Pivovarchik V, Tretter C. Location and multiplicities of eigenvalues for a star graph of Stieltjes strings. J. Difference Equ. Appl. Forthcoming 2015.
  • Stieltjes T-L. Recherches sur les fractions continues. Ann. Fac. Sci. Toulouse. 1894;8:1–122, 1895;9:1–47.
  • Krein MG, Nudelman AA. On some spectral properties of an inhomogeneous string with dissipative boundary condition. J. Oper. Theory. 1989;22:369–395. Russian.
  • Krein MG, Nudelman AA. On direct and inverse problems for frequencies of boundary dissipation of inhomogeneous string (in Russian). Doklady AN SSSR. 1979;247:1046–1049.
  • Veselić K. On linear vibrational systems with one dimensional damping I. Appl. Anal. 1988;29:1-18.
  • Veselić K. On linear vibrational systems with one dimensional damping II. Integral Equ. Oper. Theory. 1990;13:883–897.
  • Boyko O, Pivovarchik V. Inverse problem for Stieltjes string damped at one end. Methods of Funct. Anal. Topology. 2008;14:10–19.
  • Chen G, Zhou J. Vibration and damping in distributed systems. Vol. I, Analysis, estimation, attenuation, and design. Boca Raton (FL): CRC Press; 1993.
  • Kac IS, Krein MG. R-functions-analytic functions mapping the upper half-plane into itself. Amer. Math. Soc. Transl. (2) 1974;103:1–18.
  • Levin BJa. Distribution of zeros of entire functions. Vol. 5, Translations of mathematical monographs. Providence (RI): American Mathematical Society; 1980.
  • Avrachenkov KE, Filar JA, Howlett PG. Analytic perturbation theory and its applications. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM); 2013.

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