04485cam  2200517 i 450000100090000000300050000900500170001400600190003100700150005000800410006502000270010604000340013304100130016705000250018008200180020508400430022310000650026624000550033124501190038626400710050526400100057630000560058633600260064233700280066833800270069649000680072350001080079150400410089950518450094050600500278553300950283553800360293058800470296665000140301365000180302765000400304565001330308565001080321865001050332665001710343165000920360270000360369477601460373085600430387685600480391920659965RPAM20190319153332.0aa     b    000 0 cr/|||||||||||190319t20182018riua    ob    000 0 eng    a9781470450236 (online)  aDLCbengcDLCerdadDLCdRPAM1 aenghrus00aQA188b.M347513 201800a512.9/434223  a70F17a65N21a35P25a35Q70a65R322msc1 aMarchenko, V. A.q(Vladimir Aleksandrovich),d1922-eauthor.10aObratnye zadachl teorii malykh kolebaniy.lEnglish10aInverse problems in the theory of small oscillations /h[electronic resource] cVladimir Marchenko, Victor Slavin. 1aProvidence, Rhode Island :bAmerican Mathematical Society,c[2018] 4cĂ2018  a1 online resource (viii, 158 pages : illustrations)  atextbtxt2rdacontent  aunmediatedbn2rdamedia  avolumebnc2rdacarrier0 aTranslations of Mathematical Monographs, x2472-5137 ; vv. 247  aOriginally published in Russian: Obratnye Zadachl Teorii Malykh Kolebaniy (Kiev : Naukova Dumka, 2015).  aIncludes bibliographical references.00tDirect problem of the oscillation theory of loaded stringstEigenvectors of tridiagonal Hermitian matricestSpectral function of tridiagonal Hermitian matrixtSchmidt-Sonin orthogonalization processtConstruction of the tridiagonal matrix by given spectral functionstReconstruction of tridiagonal matrices by two spectratSolution methods for inverse problemstSmall oscillations, potential energy matrix and $\mathbf {L}$-matrix, direct and inverse problems of the theory of small oscillationstObservable and computable values. Reducing inverse problems of the theory of small oscillations to the inverse problem of spectral analysis for Hermitian matricestGeneral solution for the inverse problem of spectral analysis for Hermitian matricestInteraction of particles and the systems with pairwise interactionstIndecomposable systems, $\mathbf {M}$-extensions and the graph of interactionstThe main lemmatReconstructing a Hermitian matrix $\textbf {M}\in \mathfrak {M}(m)$ using its spectral data, restricted to a completely $\textbf {M}$-extendable settProperties of completely $\textbf {M}$-extendable setstExamples of $\textbf {L}$-extendable subsetstComputing masses of particles using the $\textbf {L}$-matrix of a systemtReconstructing a Hermitian matrix using its spectrum and spectra of several its perturbationstThe inverse scattering problemtSolving the inverse problem of the theory of small oscillations numericallytAnalysis of spectra for the discrete Fourier transformtComputing the coordinates of eigenvectors of an $\textbf {L}$-matrix, corresponding to observable particlestA numerical orthogonalization method for a set of vectorstA recursion for computing the coordinates for eigenvectors of an $\textbf {L}$-matrixtExamples of solving numerically the inverse problem of the theory of small oscillations1 aAccess is restricted to licensed institutions  aElectronic reproduction.bProvidence, Rhode Island :cAmerican Mathematical Society.d2018  aMode of access : World Wide Web  aDescription based on print version record. 0aMatrices. 0aOscillations. 0aFrequencies of oscillating systems. 7aMechanics of particles and systems -- Dynamics of a system of particles, including celestial mechanics -- Inverse problems.2msc 7aNumerical analysis -- Partial differential equations, boundary value problems -- Inverse problems.2msc 7aPartial differential equations -- Spectral theory and eigenvalue problems -- Scattering theory.2msc 7aPartial differential equations -- Equations of mathematical physics and other areas of application -- PDEs in connection with mechanics of particles and systems.2msc 7aNumerical analysis -- Integral equations, integral transforms -- Inverse problems.2msc1 aSlavin, Victor,d1970-eauthor.0 iPrint version: aMarchenko, V. A. 1922-tInverse problems in the theory of small oscillations /w(DLC)   2018037179x0065-9282z97814704489054 3Contentsuhttp://www.ams.org/mmono/2474 3Contentsuhttps://doi.org/10.1090/mmono/247