LEADER 02634oam 2200457 450 001 9910483706103321 005 20210417025802.0 010 $a3-030-60484-5 024 7 $a10.1007/978-3-030-60484-4 035 $a(CKB)5590000000005425 035 $a(MiAaPQ)EBC6382151 035 $a(DE-He213)978-3-030-60484-4 035 $a(PPN)258058862 035 $a(EXLCZ)995590000000005425 100 $a20210417d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDirect and inverse finite-dimensional spectral problems on graphs /$fManfred Möller, Vyacheslav Pivovarchik 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cBirkhäuser,$d[2020] 210 4$d©2020 215 $a1 online resource (XVI, 349 p.) 225 1 $aOperator Theory Advances and Applications ;$vVolume 283 311 $a3-030-60483-7 327 $aStieltjes strings -- Vibrations of star graphs -- Damped vibrations -- Trees -- Miscellaneous results -- Discrete Laplacians -- Relation between finite and infinite dimensional problems on graphs -- Rational Nevanlinna and Stieltjes Functions. 330 $aConsidering that the motion of strings with finitely many masses on them is described by difference equations, this book presents the spectral theory of such problems on finite graphs of strings. The direct problem of finding the eigenvalues as well as the inverse problem of finding strings with a prescribed spectrum are considered. This monograph gives a comprehensive and self-contained account on the subject, thereby also generalizing known results. The interplay between the representation of rational functions and their zeros and poles is at the center of the methods used. The book also unravels connections between finite dimensional and infinite dimensional spectral problems on graphs, and between self-adjoint and non-self-adjoint finite-dimensional problems. This book is addressed to researchers in spectral theory of differential and difference equations as well as physicists and engineers who may apply the presented results and methods to their research. . 410 0$aOperator theory, advances and applications ;$vVolume 283. 606 $aOperator theory 615 0$aOperator theory. 676 $a515.724 700 $aMöller$b Manfred$01065739 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bUtOrBLW 906 $aBOOK 912 $a9910483706103321 996 $aDirect and inverse finite-dimensional spectral problems on graphs$92547770 997 $aUNINA