000 05029cam a2200481Mi 4500
001 ocn958781332
003 OCoLC
005 20190328114816.0
006 m o d
007 cr unu---uuuuu
008 160917s2016 enka ob 001 0 eng d
040 _aYDX
_beng
_erda
_epn
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_dOCLCO
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019 _a958385800
_a958862794
_a959272780
_a959607242
_a960494076
_a962325695
_a962786549
020 _a9780128044704
_q(electronic bk.)
020 _a0128044705
_q(electronic bk.)
020 _z9780128044087
035 _a(OCoLC)958781332
_z(OCoLC)958385800
_z(OCoLC)958862794
_z(OCoLC)959272780
_z(OCoLC)959607242
_z(OCoLC)960494076
_z(OCoLC)962325695
_z(OCoLC)962786549
050 4 _aQA614.86
_b.M32 2016
072 7 _aMAT
_x038000
_2bisacsh
082 0 4 _a514/.742
_223
100 1 _aMassopust, Peter Robert,
_d1958-
245 1 0 _aFractal functions, fractal surfaces, and wavelets /
_h[electronic resource]
_cPeter R. Massopust.
250 _a2nd ed.
264 1 _aLondon, United Kingdom ;
_aSan Diego, CA, United States :
_bAcademic Press is an imprint of Elsevier,
_c2016.
300 _a1 online resource (428 pages)
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
588 0 _aPrint version record.
505 0 _aFront 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.
505 8 _a1 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.
505 8 _aChapter 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.
505 8 _a2 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.
505 8 _a12.1 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.
588 0 _aOnline resource; title from digital title page (viewed on September 19, 2016).
504 _aIncludes bibliographical references and index.
650 0 _aFractals.
650 7 _aMATHEMATICS
_xTopology.
_2bisacsh
650 7 _aFractals.
_2fast
_0(OCoLC)fst00933507
655 4 _aElectronic books.
776 0 8 _iPrint version:
_aMassopust, Peter R.
_tFractal Functions, Fractal Surfaces, and Wavelets.
_dSan Diego : Elsevier Science, �2016
_z9780128044087
856 4 0 _3ScienceDirect
_uhttp://www.sciencedirect.com/science/book/9780128044087
999 _c247415
_d247415