Gantmacher, F. R.; Krein, M. G. Oscillation matrices and kernels and small vibrations of mechanical systems. Translation based on the 1941 Russian original. Edited and with a preface by Alex Eremenko. Revised ed. (English) Zbl 1002.74002 Providence, RI: AMS Chelsea Publishing. viii, 310 p. (2002). This volume is a revised version of an English translation of the second edition of a book originally published in 1941 in Russian. The second edition from 1950 has been reviewed by J. L. Massera (see Zbl 0041.35502). Here, according to the preface, one finds some minor changes in the terminology and additional references. Reviewer: A.Akutowicz (Berlin) Cited in 5 ReviewsCited in 102 Documents MSC: 74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids 74H45 Vibrations in dynamical problems in solid mechanics 45B05 Fredholm integral equations 15B48 Positive matrices and their generalizations; cones of matrices 15A15 Determinants, permanents, traces, other special matrix functions 74K05 Strings 74K10 Rods (beams, columns, shafts, arches, rings, etc.) 70J50 Systems arising from the discretization of structural vibration problems 15A18 Eigenvalues, singular values, and eigenvectors Keywords:oscillatory kernel; oscillation matrices; Fredholm integral equations; sign-definite matrices; rods; strings; Sturm-Liouville equations; eigenvalues; eigenvectors; vibrations Citations:Zbl 0088.25103; Zbl 0060.03303; Zbl 0041.35502 PDF BibTeX XML Cite \textit{F. R. Gantmacher} and \textit{M. G. Krein}, Oscillation matrices and kernels and small vibrations of mechanical systems. Translation based on the 1941 Russian original. Edited and with a preface by Alex Eremenko. Revised ed. Providence, RI: AMS Chelsea Publishing (2002; Zbl 1002.74002) OpenURL