A Birman-Schwinger Principle in Galactic Dynamics

Markus Kunze (Autor)

Buch | Softcover

X, 206 Seiten

2022 | 1st ed. 2021
Springer International Publishing (Verlag)
978-3-030-75188-3 (ISBN)

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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.

Preface.- 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.

"The book is written for specialists in galactic dynamics and for mathematical physicists attracted by gravity. ... The reward comes in understanding many aspects of the Vlasov-Poisson equation in a rigorous mathematically exact way." (Marek Nowakowski, Mathematical Reviews, October, 2022)

“The book is written for specialists in galactic dynamics and for mathematical physicists attracted by gravity. … The reward comes in understanding many aspects of the Vlasov-Poisson equation in a rigorous mathematically exact way.” (Marek Nowakowski, Mathematical Reviews, October, 2022)

Erscheinungsdatum	17.08.2022
Reihe/Serie	Progress in Mathematical Physics
Zusatzinfo	X, 206 p. 3 illus., 1 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	314 g
Themenwelt	Mathematik / Informatik ► Mathematik
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Antonov Stability Estimate • Birman-Schwinger Principle • Birman-Schwinger-type Operator • Galactic Dynamics • Guo-Lin Operator • Steady State Solutions in Galactic Dynamics • Vlasov-Poisson system
ISBN-10	3-030-75188-0 / 3030751880
ISBN-13	978-3-030-75188-3 / 9783030751883
Zustand	Neuware