Massopust, Peter Robert 1958- creator text bibliography Electronic books. enk 2016 2nd ed. monographic eng

electronic resource

1 online resource (428 pages) 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 H�older spaces; 4.3 Sobolev spaces; 4.4 Besov and Triebel-Lizorkin spaces; Chapter 2: Construction of fractal sets. 1 Classical fractal sets1.1 Hausdorff measures and Hausdorff dimension; 1.2 Weierstra�-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. 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�c operator. 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. 12.1 Lebesgue spaces Lp, 0 <p 12.2 Smoothness spaces Cn and H�older 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�c 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. Peter R. Massopust. Includes bibliographical references and index. Fractals MATHEMATICS Topology Fractals QA614.86 .M32 2016 514/.742 Massopust, Peter R. San Diego : Elsevier Science, �2016 9780128044704 0128044705 http://www.sciencedirect.com/science/book/9780128044087 http://www.sciencedirect.com/science/book/9780128044087 YDX 160917 20190328114816.0 ocn958781332 eng