Fractal geometry, complex dimensions and zeta functions : geometry and spectra of fractal strings
著者
書誌事項
Fractal geometry, complex dimensions and zeta functions : geometry and spectra of fractal strings
（Springer monographs in mathematics）
Springer, c2006
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注記
Includes bibliographical references(p [413]-437) and indexes
内容説明・目次
内容説明
Number theory, spectral geometry, and fractal geometry are interlinked in this study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. The Riemann hypothesis is given a natural geometric reformulation in context of vibrating fractal strings, and the book offers explicit formulas extended to apply to the geometric, spectral and dynamic zeta functions associated with a fractal.
目次
List of Figures.- Preface.- Overview.- Introduction.- Complex Dimensions of Ordinary Fractal Strings.- Complex Dimensions of Self-Similar Fractal Strings.- Complex Dimensions of Nonlattice Self-Similar Strings: Quasiperiodic Patterns and Diophantine Approximation.- Generalized Fractal Strings Viewed as Measures.- Explicit Formulas for Generalized Fractal Strings.- The Geometry and the Spectrum of Fractal Strings.- Periodic Orbits of Self-Similar Flows.- Tubular Neighborhoods and Minkowski Measurability.- The Riemann Hypothesis and Inverse Spectral Problems.- Generalized Cantor Strings and their Oscillations.- The Critical Zeros of Zeta Functions.- Concluding Comments, Open Problems, and Perspectives.- Appendices.- A. Zeta Functions in Number Theory.- B. Zeta Functions of Laplacians and Spectral Asymptotics.- C. An Application of Nevanlinna Theory.- Bibliography.- Acknolwedgements.- Conventions.- Index of Symbols.- Author Index.- Subject Index.
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