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This 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.

Mathematical physics. --- Operator theory. --- Mathematical analysis. --- Analysis (Mathematics). --- Physics. --- Astronomy. --- Astrophysics. --- Mathematical Physics. --- Operator Theory. --- Analysis. --- Mathematical Methods in Physics. --- Astronomy, Astrophysics and Cosmology. --- Astronomical physics --- Astronomy --- Cosmic physics --- Physics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- 517.1 Mathematical analysis --- Mathematical analysis --- Functional analysis --- Physical mathematics --- Mathematics --- Física matemàtica --- Teoria quàntica --- Astrofísica --- Astronomia física --- Física astronòmica --- Astronomia --- Física --- Espectroscòpia --- Astrofísica del plasma --- Astrofísica nuclear --- Astrofísica relativista --- Atmosferes estelars --- Camps magnètics (Física còsmica) --- Col·lisions (Astrofísica) --- Cosmocronologia --- Dinàmica estel·lar --- Discos (Astrofísica) --- Electrodinàmica còsmica --- Energia fosca (Astronomia) --- Espectroscòpia astronòmica --- Expansió de l'univers --- Evolució estel·lar --- Física solar --- Jets (Astrofísica) --- Matèria interstel·lar --- Pèrdua de massa (Astrofísica) --- Transferència radiativa --- Dinàmica quàntica --- Física quàntica --- Mecànica quàntica --- Teoria dels quanta --- Teoria dels quàntums --- Dinàmica --- Mecànica de matrius --- Causalitat (Física) --- Conversions internes (Física nuclear) --- Cosmologia quàntica --- Efecte Raman --- Electrodinàmica quàntica --- Entrellaçament quàntic --- Gravetat quàntica --- Integrals de camí --- Nivells d'energia (Mecànica quàntica) --- Operador de Schrödinger --- Òptica quàntica --- Pertorbació (Dinàmica quàntica) --- Quantització geomètrica --- Quasipartícules (Física) --- Química quàntica --- Relacions de dispersió --- Renormalització (Física) --- Supergravetat --- Teoria de banda d'energia dels sòlids --- Teoria quàntica relativista --- Dinàmica molecular --- Radiació --- Termodinàmica --- Mecànica --- Acústica --- Anàlisi de sistemes --- Anàlisi dimensional --- Grups quàntics --- Elasticitat --- Equació de Yang-Baxter --- Matemàtica en l'electrònica --- Problemes de contorn --- Teoria del potencial (Física) --- Teoria ergòdica --- Teories no lineals --- Rutes aleatòries (Matemàtica) --- Galactic dynamics. --- Dynamics, Galactic --- Galaxies --- Celestial mechanics

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Operator theory --- Differential equations --- Space research --- Cosmology --- Mathematical physics --- differentiaalvergelijkingen --- analyse (wiskunde) --- wiskunde --- fysica --- ruimte (astronomie) --- kosmologie

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