LEADER 03293nam 2200565 450 001 996466406303316 005 20230427101440.0 010 $a3-030-75186-4 024 7 $a10.1007/978-3-030-75186-9 035 $a(CKB)4100000012000326 035 $a(DE-He213)978-3-030-75186-9 035 $a(MiAaPQ)EBC6700446 035 $a(Au-PeEL)EBL6700446 035 $a(PPN)257351000 035 $a(EXLCZ)994100000012000326 100 $a20220428d2021 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Birman-Schwinger principle in galactic dynamics /$fMarkus Kunze 205 $a1st ed. 2021. 210 1$aCham, Switzerland :$cBirkha?user,$d[2021] 210 4$d©2021 215 $a1 online resource (X, 206 p. 3 illus., 1 illus. in color.) 225 1 $aProgress in mathematical physics ;$vVolume 77 311 $a3-030-75185-6 320 $aIncludes bibliographical references. 327 $aPreface -- Introduction -- The Antonov Stability Estimate -- On the Period Function $T_1$ -- A Birman-Schwinger Type Operator -- Relation to the Guo-Lin Operator -- Invariances -- Appendix I: Spherical Symmetry and Action-Angle Variables -- Appendix II: Function Spaces and Operators -- Appendix III: An Evolution Equation -- Appendix IV: On Kato-Rellich Perturbation Theory. 330 $aThis monograph develops an innovative approach that utilizes the Birman-Schwinger principle from quantum mechanics to investigate stability properties of steady state solutions in galactic dynamics. The opening chapters lay the framework for the main result through detailed treatments of nonrelativistic galactic dynamics and the Vlasov-Poisson system, the Antonov stability estimate, and the period function $T_1$. Then, as the main application, the Birman-Schwinger type principle is used to characterize in which cases the ?best constant? in the Antonov stability estimate is attained. The final two chapters consider the relation to the Guo-Lin operator and invariance properties for the Vlasov-Poisson system, respectively. Several appendices are also included that cover necessary background material, such as spherically symmetric models, action-angle variables, relevant function spaces and operators, and some aspects of Kato-Rellich perturbation theory. A Birman-Schwinger Principle in Galactic Dynamics will be of interest to researchers in galactic dynamics, kinetic theory, and various aspects of quantum mechanics, as well as those in related areas of mathematical physics and applied mathematics. 410 0$aProgress in mathematical physics ;$vVolume 77. 606 $aGalactic dynamics 606 $aFísica matemàtica$2thub 606 $aTeoria quàntica$2thub 606 $aAstrofísica$2thub 608 $aLlibres electrònics$2thub 615 0$aGalactic dynamics. 615 7$aFísica matemàtica 615 7$aTeoria quàntica 615 7$aAstrofísica 676 $a523.112 700 $aKunze$b Markus$f1967-$01222547 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466406303316 996 $aA Birman-Schwinger principle in galactic dynamics$92835530 997 $aUNISA