Introduction

Michel L. Lapidus () and Machiel van Frankenhuysen ()
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Michel L. Lapidus: University of California, Department of Mathematics
Machiel van Frankenhuysen: University of California, Department of Mathematics

A chapter in Fractal Geometry and Number Theory, 2000, pp 1-6 from Springer

Abstract: Abstract A fractal drum is a bounded open subset of ℝ m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geometry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex dimensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the references therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7.1, 10.3 and 10.4, along with Appendix B.)

Keywords: Zeta Function; Complex Dimension; Riemann Zeta Function; Riemann Hypothesis; Inverse Spectral Problem (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-1-4612-5314-3_1

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