Fractal Zeta Functions and Fractal Drums
Springer International Publishing (Verlag)
978-3-319-83115-2 (ISBN)
The connections to previous extensive work of the first author and his collaborators on geometric zeta functions of fractal strings are clearly explained. Many concepts are discussed for the first time, making the book a rich source of new thoughts and ideas to be developed further. The book contains a large number of open problems and describes many possible directions for further research. The beginning chapters may be used as a part of a course on fractal geometry. The primary readership is aimed at graduate students and researchers working in Fractal Geometry and other related fields, such as Complex Analysis, Dynamical Systems, Geometric Measure Theory, Harmonic Analysis, Mathematical Physics, Analytic Number Theory and the Spectral Theory of Elliptic Differential Operators. The book should be accessible to nonexperts and newcomers to the field.
Overview.- Preface.- List of Figures.- Key Words.- Selected Key Results.- Glossary.- 1. Introduction.- 2 Distance and Tube Zeta Functions.- 3. Applications of Distance and Tube Zeta Functions.- 4. Relative Fractal Drums and Their Complex Dimensions.- 5.Fractal Tube Formulas and Complex Dimensions.- 6. Classification of Fractal Sets and Concluding Comments.- Appendix A. Tame Dirchlet-Type Integrals.- Appendix B. Local Distance Zeta Functions.- Appendix C. Distance Zeta Functions and Principal Complex Dimensions of RFDs.- Acknowledgements.- Bibliography.- Author Index.- Subject Index.
Erscheinungsdatum | 05.03.2022 |
---|---|
Reihe/Serie | Springer Monographs in Mathematics |
Zusatzinfo | XL, 655 p. 55 illus., 10 illus. in color. |
Verlagsort | Cham |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 1056 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
Naturwissenschaften ► Physik / Astronomie | |
Schlagworte | Cantor set • cone property • Dirichlet series • distance zeta function • exponent sequence • fractal drum • fractal set • fractal string • fractal zeta function • geometric zeta function • Minkowski content • Minkowski measureable • relative fractal drum • tube zeta function • zeta function |
ISBN-10 | 3-319-83115-1 / 3319831151 |
ISBN-13 | 978-3-319-83115-2 / 9783319831152 |
Zustand | Neuware |
Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
Haben Sie eine Frage zum Produkt? |
aus dem Bereich