| Edition |
Second edition. |
| Description |
1 online resource (428 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Note |
Print version record. |
| Contents |
Front Cover; Fractal Functions, Fractal Surfaces, and Wavelets; Copyright; Dedication; Contents; About the author; Preface to first edition; Preface to second edition; List of symbols; Part I: Foundations; Chapter 1: Mathematical preliminaries; 1 Analysis and topology; 2 Measures and probability theory; 3 Algebra; 3.1 Free groups, semigroups, and groups; 3.2 Reflection groups and root systems; 3.3 Affine Weyl groups and foldable figures; 4 Function spaces; 4.1 Lebesgue spaces; 4.2 Hölder spaces; 4.3 Sobolev spaces; 4.4 Besov and Triebel-Lizorkin spaces; Chapter 2: Construction of fractal sets. |
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1 Classical fractal sets1.1 Hausdorff measures and Hausdorff dimension; 1.2 Weierstraß-like fractal functions; 2 Iterated function systems; 2.1 Definition and properties of iterated function systems; 2.2 Moment theory and iterated function systems; 2.3 Recurrent iterated function systems; 2.4 Iterated Riemann surfaces; 3 Local iterated function systems; 4 Recurrent sets; 4.1 The construction of recurrent sets; 4.2 Subshifts of finite type and the connection to recurrent iterated function systems; 5 Graph-directed fractal constructions; 6 Transformations between fractal sets. |
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Chapter 3: Dimension theory1 Topological dimensions; 2 Metric dimensions; 3 Probabilistic dimensions; 4 Dimension results for self-affine fractal sets; 4.1 Dimension of self-similar fractals; 4.2 Dimension of self-affine fractals; 4.3 Recurrent iterated function systems and dimension; 4.4 Recurrent sets and Mauldin-Williams fractals; 5 The box dimension of projections; Chapter 4: Dynamical systems and dimension; 1 Ergodic theorems and entropy; 2 Lyapunov dimension; Part II: Fractal Functions and Fractal Surfaces; Chapter 5: Construction of fractal functions; 1 The Read-Bajraktarevi operator. |
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2 Local fractal functions3 Fractal bases for fractal functions; 4 Recurrent sets as fractal functions; 5 Iterative interpolation functions; 6 Recurrent fractal functions; 7 Hidden-variable fractal functions; 8 Properties of fractal functions; 8.1 Moment theory of fractal functions; 8.2 Integral transforms of fractal functions; 8.3 Lipschitz continuity of fractal functions; 8.4 Extrema of fractal functions; 9 Peano curves; 10 Fractal functions of class Ck; 10.1 Indefinite integrals of continuous fractal functions; 11 Biaffine fractal functions; 12 Local fractal functions and smoothness spaces. |
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12.1 Lebesgue spaces Lp, 0 <p 12.2 Smoothness spaces Cn and Hölder spaces Cs; 12.2.1 Binary partition of X; 12.2.2 Vanishing endpoint conditions for Si; 12.3 Sobolev spaces Wm, p; 12.4 Besov and Triebel-Lizorkin spaces; 12.4.1 Besov spaces; 12.4.2 Triebel-Lizorkin spaces; Chapter 6: Fractels and self-referential functions; 1 Fractels: definition and properties; 2 A fractel Read-Bajraktarevi operator; 3 Further properties of fractels; 3.1 Algebra; 3.2 Cartesian products and function composition; 3.3 Analysis; Chapter 7: Dimension of fractal functions; 1 Affine fractal functions 2 Recurrent fractal functions. |
| Note |
Online resource; title from digital title page (viewed on September 19, 2016). |
| Bibliography |
Includes bibliographical references and index. |
| Subject |
Fractals.
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Fractales.
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fractals.
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MATHEMATICS -- Topology.
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Fractals
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| Other Form: |
Print version: Massopust, Peter R. Fractal Functions, Fractal Surfaces, and Wavelets. San Diego : Elsevier Science, ©2016 9780128044087 |
| ISBN |
9780128044704 (electronic bk.) |
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0128044705 (electronic bk.) |
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9780128044087 |
| Standard No. |
AU@ 000058630577 |
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AU@ 000065051838 |
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AU@ 000066135360 |
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AU@ 000068129263 |
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CHNEW 001013815 |
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CHVBK 51927881X |
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DEBSZ 482473746 |
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GBVCP 879400382 |
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UKMGB 017969426 |
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