From
Grand Eagle Retail, Bensenville, IL, U.S.A.
Seller rating 5 out of 5 stars
AbeBooks Seller since 12 October 2005
Hardcover. Number theory and fractal geometry are combined in this study of the vibrations of fractal strings. The book centres around a notion of complex dimension, originally developed for the proof of the Prime Number Theorem, and extended here to apply to the zeta functions associated with fractals. Number theory and fractal geometry are combined in this study of the vibrations of fractal strings. The book centres around a notion of complex dimension extended here to apply to the zeta functions associated with fractals. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780817640989
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.
Review:
"This highly original self-contained book will appeal to geometers, fractalists, mathematical physicists and number theorists, as well as to graduate students in these fields and others interested in gaining insight into these rich areas either for its own sake or with a view to applications. They will find it a stimulating guide, well written in a clear and pleasant style."
–Mathematical Reviews (Review of First Edition)
"It is the reviewer’s opinion that the authors have succeeded in showing that the complex dimensions provide a very natural and unifying mathematical framework for investigating the oscillations in the geometry and the spectrum of a fractal string. The book is well written. The exposition is self-contained, intelligent and well paced."
–Bulletin of the London Mathematical Society (Review of First Edition)
"The new approach and results on the important problems illuminated in this work will appeal to researchers and graduate students in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics."
–Simulation News Europe (Review of First Edition)
Title: Fractal Geometry and Number Theory (...
Publisher: Birkhauser Boston, Berlin
Publication Date: 1999
Binding: Hardcover
Condition: new
Seller: Jenson Books Inc, Logan, UT, U.S.A.
hardcover. Condition: Very Good. A clean, cared for item that is unmarked and shows limited shelf wear. Seller Inventory # 4BQWN80009QI
Quantity: 1 available
Seller: moluna, Greven, Germany
Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 1 Complex Dimensions of Ordinary Fractal Strings.- 1.1 The Geometry of a Fractal String.- 1.1.1 The Multiplicity of the Lengths.- 1.1.2 Example: The Cantor String.- 1.2 The Geometric Zeta Function of a Fractal String.- 1.2.1 The Screen and the Window.- 1.2. Seller Inventory # 5975648
Quantity: Over 20 available
Seller: preigu, Osnabrück, Germany
Buch. Condition: Neu. Fractal Geometry and Number Theory | Complex Dimensions of Fractal Strings and Zeros of Zeta Functions | Machiel van Frankenhuysen (u. a.) | Buch | xii | Englisch | 1999 | Birkhäuser Boston | EAN 9780817640989 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. Seller Inventory # 106790115
Quantity: 5 available
Seller: Lucky's Textbooks, Dallas, TX, U.S.A.
Condition: New. Seller Inventory # ABLIING23Feb2416190237508
Quantity: Over 20 available
Seller: GreatBookPrices, Columbia, MD, U.S.A.
Condition: New. Seller Inventory # 206886-n
Quantity: Over 20 available
Seller: buchversandmimpf2000, Emtmannsberg, BAYE, Germany
Buch. Condition: Neu. Neuware -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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 284 pp. Englisch. Seller Inventory # 9780817640989
Quantity: 2 available
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 284 pp. Englisch. Seller Inventory # 9780817640989
Quantity: 2 available
Seller: GreatBookPricesUK, Woodford Green, United Kingdom
Condition: New. Seller Inventory # 206886-n
Quantity: Over 20 available
Seller: Ria Christie Collections, Uxbridge, United Kingdom
Condition: New. In. Seller Inventory # ria9780817640989_new
Quantity: Over 20 available
Seller: California Books, Miami, FL, U.S.A.
Condition: New. Seller Inventory # I-9780817640989
Quantity: Over 20 available