Lapidus, M.L., Frankenhuijsen, M.V. 　著

内容

目次

List of Figures.- Preface.- Overview.- Introduction.- Complex Dimensionsof Ordinary Fractal Strings.- Complex Dimensions of Self-Similar FractalStrings.- Complex Dimensions of Nonlattice Self-Similar Strings:Quasiperiodic Patterns and Diophantine Approximation.- Generalized FractalStrings Viewed as Measures.- Explicit Formulas for Generalized FractalStrings.- The Geometry and the Spectrum of Fractal Strings.- Periodic Orbitsof Self-Similar Flows.- Tubular Neighborhoods and Minkowski Measurability.-The Riemann Hypothesis and Inverse Spectral Problems.- Generalized CantorStrings and their Oscillations.- The Critical Zeros of Zeta Functions.-Concluding Comments, Open Problems, and Perspectives.- Appendices.- A. ZetaFunctions in Number Theory.- B. Zeta Functions of Laplacians and SpectralAsymptotics.- C. An Application of Nevanlinna Theory.- Bibliography.-Acknolwedgements.- Conventions.- Index of Symbols.- Author Index.- SubjectIndex.