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 (geo- metry) 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 di- mensions 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 ...
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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 (geo- metry) 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 di- mensions 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 ref- erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap- pendix B. ) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which form a sequence which we assume to be infinite. Important information about the geometry of . c is contained in its geometric zeta function (c(8) = L lj. j=l 2 Introduction We assume throughout that this function has a suitable meromorphic ex- tension. The central notion of this book, the complex dimensions of a fractal string . c, is defined as the poles of the meromorphic extension of (c.
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Add this copy of Fractal Geometry and Number Theory: Complex Dimensions to cart. $34.83, very good condition, Sold by Jenson Books Inc rated 4.0 out of 5 stars, ships from Logan, UT, UNITED STATES, published 1999 by Birkhauser.
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Add this copy of Fractal Geometry and Number Theory: Complex Dimensions to cart. $51.65, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 1999 by Birkhauser.
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Add this copy of Fractal Geometry and Number Theory: Complex Dimensions to cart. $71.22, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 1999 by Birkhauser.
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Add this copy of Fractal Geometry and Number Theory to cart. $120.67, new condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 1999 by Birkhäuser.
