Abstract
A fractal drum is a bounded open subset of ℝm 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 fractal strings, and we study how these complex dimensions relate the geometry and the spectrum of fractal strings. See the notes to Chapter 1 in Section 1.5 for references to the literature.
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© 2006 Springer Science+Business Media, LLC
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(2006). Introduction. In: Fractal Geometry, Complex Dimensions and Zeta Functions. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-35208-4_1
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DOI: https://doi.org/10.1007/978-0-387-35208-4_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-33285-7
Online ISBN: 978-0-387-35208-4
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