WorldCat Identities

Van Frankenhuysen, Machiel 1967-

Overview
Works: 16 works in 123 publications in 2 languages and 2,447 library holdings
Genres: Conference papers and proceedings 
Roles: Author, Editor, Correspondent
Classifications: QA614.86, 514.742
Publication Timeline
.
Most widely held works by Machiel Van Frankenhuysen
Fractal geometry and number theory : complex dimensions of fractal strings and zeros of zeta functions, with 26 illustrations by Michel L Lapidus( Book )

19 editions published between 1999 and 2012 in English and held by 330 WorldCat member libraries worldwide

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
Fractal geometry, complex dimensions and zeta functions : geometry and spectra of fractal strings by Michel L Lapidus( Book )

20 editions published between 2006 and 2013 in English and held by 319 WorldCat member libraries worldwide

Offers a study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. This book interlinks number theory, spectral geometry, and fractal geometry. It gives the Riemann hypothesis a natural geometric reformulation in the context of vibrating fractal strings. It includes theorems, examples and illustrations
Fractal geometry and applications : a jubilee of Benoît Mandelbrot( Book )

39 editions published in 2004 in English and held by 317 WorldCat member libraries worldwide

Dynamical, spectral, and arithmetic zeta functions : AMS Special Session on Dynamical, Spectral, and Arithmetic Zeta Functions, January 15-16, 1999, San Antonio, Texas by spectral, and arithmetic Zeta functions AMS Special session on dynamical( Book )

9 editions published between 2001 and 2002 in English and held by 204 WorldCat member libraries worldwide

The Riemann hypothesis for function fields : Frobenius flow and shift operators by Machiel Van Frankenhuysen( Book )

15 editions published between 2013 and 2014 in English and held by 158 WorldCat member libraries worldwide

A graduate-level description of how ideas from non-commutative geometry could provide a means to attack the Riemann hypothesis, one of the most important conjectures in mathematics. The book provides a strong foundation for further research in this area
Fractal geometry and dynamical systems in pure and applied mathematics by PISRS (Conference)( Book )

8 editions published in 2013 in English and held by 103 WorldCat member libraries worldwide

Hyperbolic spaces and the abc conjecture by Machiel Van Frankenhuysen( Book )

3 editions published in 1995 in English and Undetermined and held by 13 WorldCat member libraries worldwide

Mijmeringen in den strijd der voor- en tegenstanders der vigeerende wet op 't onderwijs by Frankenhuysen( Book )

2 editions published in 1886 in Dutch and held by 2 WorldCat member libraries worldwide

Complex dimensions and oscillatory phenomena, with applications to the geometry of fractal strings and the critical zeros of zeta-functions by Michel L Lapidus( Book )

2 editions published in 1997 in English and held by 2 WorldCat member libraries worldwide

Brief van van Frankenhuysen aan Johannes Christoffel Schultz Jacobi (1806-1865) by Machiel Van Frankenhuysen( )

1 edition published in 1852 in Undetermined and held by 1 WorldCat member library worldwide

Good abc examples over number fields by Machiel Van Frankenhuysen( Book )

1 edition published in 1997 in English and held by 1 WorldCat member library worldwide

Leesstukken( Book )

1 edition published in 1976 in Dutch and held by 1 WorldCat member library worldwide

Complex dimensions of fractal strings and explicit formulas for geometric and spectral zeta-functions by Michel L Lapidus( Book )

1 edition published in 1997 in English and held by 1 WorldCat member library worldwide

Complex dimensions of fractal strings and oscillatory phenomena in geometry and arithmetic by Michel L Lapidus( Book )

1 edition published in 1997 in English and held by 1 WorldCat member library worldwide

Fractal geometry and dynamical systems in pure and applied mathematics( )

in English and held by 0 WorldCat member libraries worldwide

 
moreShow More Titles
fewerShow Fewer Titles
Audience Level
0
Audience Level
1
  Kids General Special  
Audience level: 0.64 (from 0.52 for Fractal ge ... to 0.97 for Fractal ge ...)

Fractal geometry and number theory : complex dimensions of fractal strings and zeros of zeta functions, with 26 illustrations
Alternative Names
Frankenhuijsen, Machiel van.

Frankenhuijsen, Machiel van 1967-

Frankenhuysen, M. van 1967-

Frankenhuysen, Machiel van.

Frankenhuysen Machiel van 1967-....

Machiel Frankenhuysen

Machiel van Frankenhuijsen

Machiel van Frankenhuijsen niederländischer Mathematiker

Machiel van Frankenhuysen

Van Frankenhuijsen, Machiel.

Van Frankenhuijsen, Machiel 1967-

Van Frankenhuysen, Machiel

Van Frankenhuysen, Machiel 1967-

Languages
English (118)

Dutch (3)

Covers
Fractal geometry, complex dimensions and zeta functions : geometry and spectra of fractal stringsFractal geometry and applications : a jubilee of Benoît MandelbrotDynamical, spectral, and arithmetic zeta functions : AMS Special Session on Dynamical, Spectral, and Arithmetic Zeta Functions, January 15-16, 1999, San Antonio, Texas