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Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions - Couverture rigide
Synopsis
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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Fractal Geometry and Number Theory
Edité par
Birkhäuser, 1999
ISBN 10 : 0817640983
ISBN 13 : 9780817640989
Ancien ou d'occasion
Couverture rigide
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hardcover. Etat : Very Good. A clean, cared for item that is unmarked and shows limited shelf wear. N° de réf. du vendeur 4BQWN80009QI
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Fractal Geometry and Number Theory : Complex Dimensions of Fractal Strings and Zeros and Zeta-Functions
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Fractal Geometry and Number Theory
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Fractal Geometry and Number Theory (Hardcover)
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Birkhauser Boston, Berlin, 1999
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ISBN 13 : 9780817640989
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Couverture rigide
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Hardcover. Etat : new. 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. N° de réf. du vendeur 9780817640989
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Fractal Geometry and Number Theory
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Fractal Geometry and Number Theory : Complex Dimensions of Fractal Strings and Zeros and Zeta-Functions
Edité par
Birkhäuser, 1999
ISBN 10 : 0817640983
ISBN 13 : 9780817640989
Ancien ou d'occasion
Couverture rigide
Vendeur : GreatBookPrices, Columbia, MD, Etats-Unis
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Fractal Geometry and Number Theory
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Fractal Geometry and Number Theory
Edité par
Birkhäuser Boston Dez 1999, 1999
ISBN 10 : 0817640983
ISBN 13 : 9780817640989
Neuf
Couverture rigide
Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
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Buch. Etat : 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. N° de réf. du vendeur 9780817640989
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Fractal Geometry and Number Theory : Complex Dimensions of Fractal Strings and Zeros and Zeta-Functions
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Fractal Geometry and Number Theory
Edité par
Springer Science & Business Media, 1999
ISBN 10 : 0817640983
ISBN 13 : 9780817640989
Neuf
Couverture souple
Vendeur : Agapea Libros, Malaga, MA, Espagne
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Etat : New. Idioma/Language: Inglés. 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. *** Nota: Los envíos a España peninsular, Baleares y Canarias se realizan a través de mensajería urgente. No aceptamos pedidos con destino a Ceuta y Melilla. N° de réf. du vendeur 888761
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