05029cam a2200481Mi 4500 ocn958781332 OCoLC 20190328114816.0 m o d cr unu---uuuuu 160917s2016 enka ob 001 0 eng d YDX eng rda pn YDX OCLCO EBLCP OPELS IDEBK TEFOD OCLCF OCLCQ IDB DEBSZ N$T OCLCQ U3W MERUC D6H OCLCQ TKN 958385800 958862794 959272780 959607242 960494076 962325695 962786549 9780128044704 (electronic bk.) 0128044705 (electronic bk.) 9780128044087 (OCoLC)958781332 (OCoLC)958385800 (OCoLC)958862794 (OCoLC)959272780 (OCoLC)959607242 (OCoLC)960494076 (OCoLC)962325695 (OCoLC)962786549 QA614.86 .M32 2016 MAT 038000 bisacsh 514/.742 23 Massopust, Peter Robert, 1958- Fractal functions, fractal surfaces, and wavelets / [electronic resource] Peter R. Massopust. 2nd ed. London, United Kingdom ; San Diego, CA, United States : Academic Press is an imprint of Elsevier, 2016. 1 online resource (428 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Print version record. 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. Online resource; title from digital title page (viewed on September 19, 2016). Includes bibliographical references and index. Fractals. MATHEMATICS Topology. bisacsh Fractals. fast (OCoLC)fst00933507 Electronic books. Print version: Massopust, Peter R. Fractal Functions, Fractal Surfaces, and Wavelets. San Diego : Elsevier Science, �2016 9780128044087 ScienceDirect http://www.sciencedirect.com/science/book/9780128044087 247415 247415