Kooperativer Bibliotheksverbund

UID:

Format: X, 397 S , Ill., graph. Darst

ISBN: 0821808753

Series Statement: CRM proceedings and lecture notes 18

Note: Includes bibliographical references

Language: English

Subjects: Mathematics

Keywords: Spline-Funktion ; Wavelet

URL: Inhaltsverzeichnis

URL: Inhaltstext

UID:

Format: 1 Online-Ressource (XV, 472 p)

ISBN: 9789401579315 , 9789401579339

Series Statement: NATO ASI Series, Series C: Mathematical and Physical Sciences 346

Note: This ASI- which was also the 28th session of the Seminaire de mathematiques superieures of the Universite de Montreal - was devoted to Fractal Geometry and Analysis. The present volume is the fruit of the work of this Advanced Study Institute. We were fortunate to have with us Prof. Benoit Mandelbrot - the creator of numerous concepts in Fractal Geometry - who gave a series of lectures on multifractals, iteration of analytic functions, and various kinds of fractal stochastic processes. Different foundational contributions for Fractal Geometry like measure theory, dy­ namical systems, iteration theory, branching processes are recognized. The geometry of fractal sets and the analytical tools used to investigate them provide a unifying theme of this book. The main topics that are covered are then as follows. Dimension Theory. Many definitions of fractional dimension have been proposed, all of which coincide on "regular" objects, but often take different values for a given fractal set. There is ample discussion on piecewise estimates yielding actual values for the most common dimensions (Hausdorff, box-counting and packing dimensions). The dimension theory is mainly discussed by Mendes-France, Bedford, Falconer, Tricot and Rata. Construction of fractal sets. Scale in variance is a fundamental property of fractal sets

Language: English

Keywords: Fraktal ; Konferenzschrift

DOI: 10.1007/978-94-015-7931-5

URL: Volltext

UID:

Format: 1 online resource (x, 397 p. : ill.)

Edition: Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

ISBN: 9781470439323 (online)

Series Statement: CRM Proceedings and Lecture Notes, v. 18

Note: Introduction and summary , Radial extensions of vertex data , The use of splines in the numerical solutions of differential and Volterra integral equations , On best error bounds for deficient splines , Optimal error bounds for spline interpolation on a uniform partition , Modelization of flexible objects using constrained optimization and B-spline surfaces , New control polygons for polynomial curves , Splines in approximation and differential operators: $(m,\ell ,s)$ interpolating-spline , New families of B-splines on uniform meshes of the plane , Introduction and summary , Analysis of Hermite-interpolatory subdivision schemes , Some directional microlocal classes defined using wavelet transforms , Nonseparable biorthogonal wavelet bases of $L^2(\mathbb R^n)$ , Local bases: Theory and applications , On the $L^p$-Lipschitz exponents of the scaling functions , Robust speech and speaker recognition using instantaneous frequencies and amplitudes obtained with wavelet-derived synchrosqueezing measures , Extensions of the Heisenberg group and wavelet analysis in the plane , Introduction and summary , Coherent states and quantization , Wavelets in molecular and condensed-matter physics , Wavelets in atomic physics , The wavelet $\epsilon $-expansion and Hausdorff dimension , Modelling the coupling between small and large scales in the Kuramoto-Sivashinsky equation , Continuous wavelet transform analysis of one-dimensional quantum ground states , Oscillating singularities and fractal functions , Introduction and summary , Wavelet estimators for change-point regression models , Wavelet thresholding for non (necessarily) Guassian noise: A preliminary report , Deslauries-Dubuc: Ten years after , Some theory for $L$-spline smoothing , Spectral representation and estimation for locally stationary wavelet processes , Mode of access : World Wide Web

Additional Edition: Print version: Spline functions and the theory of wavelets / ISSN 1065-8580 ISBN 9780821808757

Language: English

URL: Contents

URL: Contents

UID:

Format: XV, 472 p. 85 illus. , online resource.

Edition: 1st ed. 1991.

ISBN: 9789401579315

Series Statement: Nato Science Series C:, Mathematical and Physical Sciences ; 346

Content: This ASI- which was also the 28th session of the Seminaire de mathematiques superieures of the Universite de Montreal - was devoted to Fractal Geometry and Analysis. The present volume is the fruit of the work of this Advanced Study Institute. We were fortunate to have with us Prof. Benoit Mandelbrot - the creator of numerous concepts in Fractal Geometry - who gave a series of lectures on multifractals, iteration of analytic functions, and various kinds of fractal stochastic processes. Different foundational contributions for Fractal Geometry like measure theory, dy­ namical systems, iteration theory, branching processes are recognized. The geometry of fractal sets and the analytical tools used to investigate them provide a unifying theme of this book. The main topics that are covered are then as follows. Dimension Theory. Many definitions of fractional dimension have been proposed, all of which coincide on "regular" objects, but often take different values for a given fractal set. There is ample discussion on piecewise estimates yielding actual values for the most common dimensions (Hausdorff, box-counting and packing dimensions). The dimension theory is mainly discussed by Mendes-France, Bedford, Falconer, Tricot and Rata. Construction of fractal sets. Scale in variance is a fundamental property of fractal sets.

Note: Applications of dynamical systems theory to fractals - a study of cookie-cutter Cantor sets -- Complex dynamics: an informal discussion -- Substitutions, branching processes and fractal sets -- Interpolation fractale -- Dimensions - their determination and properties -- Topological aspects of self-similar sets and singular functions -- Produits de poids aléatoires indépendants et applications -- The Planck constant of a curve -- Rectifiable and fractal sets -- Iterated function systems: theory, applications and the inverse problem.

In: Springer Nature eBook

Additional Edition: Printed edition: ISBN 9789401579339

Additional Edition: Printed edition: ISBN 9789401579322

Additional Edition: Printed edition: ISBN 9780792313991

Language: English

DOI: 10.1007/978-94-015-7931-5

URL: https://doi.org/10.1007/978-94-015-7931-5