{"product_id":"inverse-problems-in-the-theory-of-small-oscillations-hardback-9781470448905","title":"Inverse Problems in the Theory of Small Oscillations (Hardback) 9781470448905","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eInverse Problems in the Theory of Small Oscillations\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eVladimir Marchenko (Author), Victor Slavin (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781470448905\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 30 December 2018\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e176 pages\u003cbr\u003e25.4 x 17.8 x 2 cm, 0.448 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eInverse problems of spectral analysis deal with the reconstruction of operators of the specified form in Hilbert or Banach spaces from certain of their spectral characteristics. An interest in spectral problems was initially inspired by quantum mechanics. The main inverse spectral problems have been solved already for Schrodinger operators and for their finite-difference analogues, Jacobi matrices.\u003cbr\u003e\u003cbr\u003eThis book treats inverse problems in the theory of small oscillations of systems with finitely many degrees of freedom, which requires finding the potential energy of a system from the observations of its oscillations. Since oscillations are small, the potential energy is given by a positive definite quadratic form whose matrix is called the matrix of potential energy. Hence, the problem is to find a matrix belonging to the class of all positive definite matrices. This is the main difference between inverse problems studied in this book and the inverse problems for discrete analogues of the Schrodinger operators, where only the class of tridiagonal Hermitian matrices are considered.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cul\u003e\n\u003cli\u003eDirect problem of the oscillation theory of loaded strings\u003c\/li\u003e\n\u003cli\u003eEigenvectors of tridiagonal Hermitian matrices\u003c\/li\u003e\n\u003cli\u003eSpectral function of tridiagonal Hermitian matrix\u003c\/li\u003e\n\u003cli\u003eSchmidt-Sonin orthogonalization process\u003c\/li\u003e\n\u003cli\u003eConstruction of the tridiagonal matrix by given spectral functions\u003c\/li\u003e\n\u003cli\u003eReconstruction of tridiagonal matrices by two spectra\u003c\/li\u003e\n\u003cli\u003eSolution methods for inverse problems\u003c\/li\u003e\n\u003cli\u003eSmall oscillations, potential energy matrix and $\\mathbf{L}$-matrix, direct and inverse problems of the theory of small oscillations\u003c\/li\u003e\n\u003cli\u003eObservable and computable values. Reducing inverse problems of the theory of small oscillations to the inverse problem of spectral analysis for Hermitian matrices\u003c\/li\u003e\n\u003cli\u003eGeneral solution for the inverse problem of spectral analysis for Hermitian matrices\u003c\/li\u003e\n\u003cli\u003eInteraction of particles and the systems with pairwise interactions\u003c\/li\u003e\n\u003cli\u003eIndecomposable systems, $\\mathbf{M}$-extensions and the graph of interactions\u003c\/li\u003e\n\u003cli\u003eThe main lemma\u003c\/li\u003e\n\u003cli\u003eReconstructing a Hermitian matrix $\\textbf{M}\\in\\mathfrak{M}(m)$ using its spectral data, restricted to a completely $\\textbf{M}$-extendable set\u003c\/li\u003e\n\u003cli\u003eThe properties of completely $\\textbf{M}$-extendable sets\u003c\/li\u003e\n\u003cli\u003eThe examples of $\\textbf{L}$-extendable subsets\u003c\/li\u003e\n\u003cli\u003eComputing masses of particles using the $\\textbf{L}$-matrix of a system\u003c\/li\u003e\n\u003cli\u003eReconstructing a Hermitian matrix using its spectrum and spectra of several its perturbations\u003c\/li\u003e\n\u003cli\u003eThe inverse scattering problem\u003c\/li\u003e\n\u003cli\u003eSolving the inverse problem of the theory of small oscillations numerically\u003c\/li\u003e\n\u003cli\u003eAnalysis of spectra for the discrete Fourier transform\u003c\/li\u003e\n\u003cli\u003eComputing the coordinates of eigenvectors of an $\\textbf{L}$-matrix, corresponding to observable particles\u003c\/li\u003e\n\u003cli\u003eA numerical orthogonalization method for a set of vectors\u003c\/li\u003e\n\u003cli\u003eA recursion for computing the coordinates for eigenvectors of an $\\textbf{L}$-matrix\u003c\/li\u003e\n\u003cli\u003eThe examples of solving numerically the inverse problem of the theory of small oscillations\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cul\u003e\u003c\/ul\u003e\n\u003c\/ul\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003c\/font\u003e","brand":"American Mathematical Society","offers":[{"title":"Brand New","offer_id":52589078216984,"sku":"9781470448905","price":102.59,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/freshlyprintedbooks.co.uk\/products\/inverse-problems-in-the-theory-of-small-oscillations-hardback-9781470448905","provider":"Freshly Printed Books","version":"1.0","type":"link"}