Description: Fractal Geometry and Number Theory : Complex Dimensions of Fractal Strings and Zeros and Zeta-Functions, Hardcover by Lapidus, Michel L.; Van Frankenhuysen, Machiel, ISBN 0817640983, ISBN-13 9780817640989, Brand New, Free shipping in the US 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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Book Title: Fractal Geometry and Number Theory : Complex Dimensions of Fracta
Number of Pages: Xii, 268 Pages
Publication Name: Fractal Geometry and Number Theory : Complex Dimensions of Fractal Strings and Zeros of Zeta Functions
Language: English
Publisher: Birkhäuser Boston
Item Height: 0.3 in
Subject: Geometry / Differential, Functional Analysis, Geometry / General, Number Theory, Geometry / Algebraic
Publication Year: 1999
Item Weight: 44.8 Oz
Type: Textbook
Subject Area: Mathematics
Item Length: 9.3 in
Author: Machiel Van Frankenhuysen, Michel L. Lapidus
Item Width: 6.1 in
Format: Hardcover
