Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings (Hardcover)

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. 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.