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Inverse problems for Jacobi operators III: Mass-spring perturbations of semi-infinite systems
1. | Departamento de Métodos Matemáticos y Numéricos, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, C.P. 04510, México D.F., Mexico, Mexico |
2. | Department of Mathematics, Institute for Low Temperature Physics and Engineering, Lenin Av. 47, 61103, Kharkov, Ukraine |
References:
[1] |
N. I. Akhiezer, “The Classical Moment Problem and Some Related Questions in Analysis,'' Hafner Publishing Co., New York, 1965. |
[2] |
N. I. Akhiezer and I. M. Glazman, "Theory of Linear Operators in Hilbert Space,'' Dover Publications, Inc., New York, 1993. |
[3] |
Ju. M. Berezans'kiĭ, "Expansions in eigenfunctions of selfadjoint operators,'' Translations of Mathematical Monographs, 17, American Mathematical Society, Providence, R.I., 1968. |
[4] |
M. Sh. Birman and M. Z. Solomjak, "Spectral Theory of Selfadjoint Operators in Hilbert Space,'' Mathematics and its Applications (Soviet Series), D. Reidel Publishing Co., Dordrecht, 1987. |
[5] |
M. T. Chu and G. H. Golub, "Inverse Eigenvalue Problems: Theory Algorithms and Applications,'' Numerical Mathematics and Scientific Computation, Oxford University Press, New York, 2005. |
[6] |
C. de Boor and G. H. Golub, The numerically stable reconstruction of a Jacobi matrix from spectral data, Linear Alg. Appl., 21 (1978), 245-260. |
[7] |
R. del Rio and M. Kudryavtsev, Inverse problems for Jacobi operators I: Interior mass-spring perturbations in finite systems, arXiv:1106.1691. |
[8] |
R. del Rio, M. Kudryavtsev and L. O. Silva, Inverse problems for Jacobi operators II: Mass perturbations of semi-infinite mass-spring systems, arXiv:1106.4598. |
[9] |
L. Fu and H. Hochstadt, Inverse theorems for Jacobi matrices, J. Math. Anal. Appl., 47 (1974), 162-168.
doi: 10.1016/0022-247X(74)90044-4. |
[10] |
F. Gesztesy and B. Simon, $m$-functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices, J. Anal. Math., 73 (1997), 267-297.
doi: 10.1007/BF02788147. |
[11] |
G. M. L. Gladwell, "Inverse Problems in Vibration,'' Second edition, Solid Mechanics and its Applications, 119, Kluwer Academic Publishers, Dordrecht, 2004. |
[12] |
R. Z. Halilova, An inverse problem, (Russian), Izv. Akad. Nauk Azerbaĭ džan, SSR Ser. Fiz.-Tehn. Mat. Nauk, 1967 (1967), 169-175. |
[13] |
B. Ja. Levin, "Distribution of Zeros of Entire Functions,'' Translations of Mathematical Monographs, 5, American Mathematical Society, Providence, R.I., 1980. |
[14] |
V. A. Marchenko and T. V. Misyura, "Señalamientos Metodológicos y Didácticos al Tema: Problemas Inversos de la Teoría Espectral de Operadores de Dimensión Finita,'' Monografías IIMAS-UNAM, 12, No. 28, México, 2004. |
[15] |
Y. M. Ram, Inverse eigenvalue problem for a modified vibrating system, SIAM Appl. Math., 53 (1993), 1762-1775. |
[16] |
L. O. Silva and R. Weder, On the two spectra inverse problem for semi-infinite Jacobi matrices, Math. Phys. Anal. Geom., 9 (2006), 263-290. |
[17] |
B. Simon, The classical moment problem as a self-adjoint finite difference operator, Adv. Math., 137 (1998), 82-203. |
[18] |
M. Spletzer, A. Raman, H. Sumali and J. P. Sullivan, Highly sensitive mass detection and identification using vibration localization in coupled microcantilever arrays, Applied Physics Letters, 92 (2008), 114102. |
[19] |
M. Spletzer, A. Raman, A. Q. Wu and X. Xu, Ultrasensitive mass sensing using mode localization in coupled microcantilevers, Applied Physics Letters, 88 (2006), 254102. |
[20] |
G. Teschl, Trace formulas and inverse spectral theory for Jacobi operators, Comm. Math. Phys., 196 (1998), 175-202. |
[21] |
G. Teschl, "Jacobi Operators and Completely Integrable Nonlinear Lattices,'' Mathematical Surveys and Monographs, 72, American Mathematical Society, Providence, RI, 2000. |
show all references
References:
[1] |
N. I. Akhiezer, “The Classical Moment Problem and Some Related Questions in Analysis,'' Hafner Publishing Co., New York, 1965. |
[2] |
N. I. Akhiezer and I. M. Glazman, "Theory of Linear Operators in Hilbert Space,'' Dover Publications, Inc., New York, 1993. |
[3] |
Ju. M. Berezans'kiĭ, "Expansions in eigenfunctions of selfadjoint operators,'' Translations of Mathematical Monographs, 17, American Mathematical Society, Providence, R.I., 1968. |
[4] |
M. Sh. Birman and M. Z. Solomjak, "Spectral Theory of Selfadjoint Operators in Hilbert Space,'' Mathematics and its Applications (Soviet Series), D. Reidel Publishing Co., Dordrecht, 1987. |
[5] |
M. T. Chu and G. H. Golub, "Inverse Eigenvalue Problems: Theory Algorithms and Applications,'' Numerical Mathematics and Scientific Computation, Oxford University Press, New York, 2005. |
[6] |
C. de Boor and G. H. Golub, The numerically stable reconstruction of a Jacobi matrix from spectral data, Linear Alg. Appl., 21 (1978), 245-260. |
[7] |
R. del Rio and M. Kudryavtsev, Inverse problems for Jacobi operators I: Interior mass-spring perturbations in finite systems, arXiv:1106.1691. |
[8] |
R. del Rio, M. Kudryavtsev and L. O. Silva, Inverse problems for Jacobi operators II: Mass perturbations of semi-infinite mass-spring systems, arXiv:1106.4598. |
[9] |
L. Fu and H. Hochstadt, Inverse theorems for Jacobi matrices, J. Math. Anal. Appl., 47 (1974), 162-168.
doi: 10.1016/0022-247X(74)90044-4. |
[10] |
F. Gesztesy and B. Simon, $m$-functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices, J. Anal. Math., 73 (1997), 267-297.
doi: 10.1007/BF02788147. |
[11] |
G. M. L. Gladwell, "Inverse Problems in Vibration,'' Second edition, Solid Mechanics and its Applications, 119, Kluwer Academic Publishers, Dordrecht, 2004. |
[12] |
R. Z. Halilova, An inverse problem, (Russian), Izv. Akad. Nauk Azerbaĭ džan, SSR Ser. Fiz.-Tehn. Mat. Nauk, 1967 (1967), 169-175. |
[13] |
B. Ja. Levin, "Distribution of Zeros of Entire Functions,'' Translations of Mathematical Monographs, 5, American Mathematical Society, Providence, R.I., 1980. |
[14] |
V. A. Marchenko and T. V. Misyura, "Señalamientos Metodológicos y Didácticos al Tema: Problemas Inversos de la Teoría Espectral de Operadores de Dimensión Finita,'' Monografías IIMAS-UNAM, 12, No. 28, México, 2004. |
[15] |
Y. M. Ram, Inverse eigenvalue problem for a modified vibrating system, SIAM Appl. Math., 53 (1993), 1762-1775. |
[16] |
L. O. Silva and R. Weder, On the two spectra inverse problem for semi-infinite Jacobi matrices, Math. Phys. Anal. Geom., 9 (2006), 263-290. |
[17] |
B. Simon, The classical moment problem as a self-adjoint finite difference operator, Adv. Math., 137 (1998), 82-203. |
[18] |
M. Spletzer, A. Raman, H. Sumali and J. P. Sullivan, Highly sensitive mass detection and identification using vibration localization in coupled microcantilever arrays, Applied Physics Letters, 92 (2008), 114102. |
[19] |
M. Spletzer, A. Raman, A. Q. Wu and X. Xu, Ultrasensitive mass sensing using mode localization in coupled microcantilevers, Applied Physics Letters, 88 (2006), 254102. |
[20] |
G. Teschl, Trace formulas and inverse spectral theory for Jacobi operators, Comm. Math. Phys., 196 (1998), 175-202. |
[21] |
G. Teschl, "Jacobi Operators and Completely Integrable Nonlinear Lattices,'' Mathematical Surveys and Monographs, 72, American Mathematical Society, Providence, RI, 2000. |
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