Opening book details…
Can I read Fractal Geometry and Number Theory : Complex Dimensions of Fractal Strings and Zeros of Zeta Functions, with 26 Illustrations on EtoBox?
Fractal Geometry and Number Theory : Complex Dimensions of Fractal Strings and Zeros of Zeta Functions, with 26 Illustrations by Michel L. Lapidus, Michel Laurent Lapidus, Machiel van Frankenhuysen is a nonfiction available to read on EtoBox.
What is Fractal Geometry and Number Theory : Complex Dimensions of Fractal Strings and Zeros of Zeta Functions, with 26 Illustrations about?
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 assu
Who reads Fractal Geometry and Number Theory : Complex Dimensions of Fractal Strings and Zeros of Zeta Functions, with 26 Illustrations?
It is typically read by self-directed learners exploring a subject in depth.
Common subject areas: history, science, philosophy, social sciences.
- Author
- Michel L. Lapidus, Michel Laurent Lapidus, Machiel van Frankenhuysen
- Publisher
- Springer Science & Business Media
- Published
- 2000
- Language
- EN
- ISBN
- 9783764340988
- Category
- nonfiction
- Subjects
- Mathematics, Geometry And Topology, Stem
Other editions & translations
More by Michel L. Lapidus, Michel Laurent Lapidus, Machiel van Frankenhuysen
Browse all works by Michel L. Lapidus, Michel Laurent Lapidus, Machiel van Frankenhuysen
Similar books
- Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings (Springer Monographs in Mathematics) — Lapidus M Et Al (2006)
- Fractal Zeta Functions and Fractal Drums : Higher-Dimensional Theory of Complex Dimensions — Michel L. Lapidus, Goran Radunović and Darko Žubrinić (2017)
- Generalized Minkowski Content, Spectrum of Fractal Drums, Fractal Strings and the Riemann Zeta-Functions — Christina Q. He; Michel Laurent Lapidus (1997)