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Kahane J.-P. — Fourier Series and Wavelets, Vol. 3

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Название: Fourier Series and Wavelets, Vol. 3

Автор: Kahane J.-P.

Аннотация:

This comprehensive monograph presents the history and achievements of one of the most important figures in modern mathematics, covering the work of Fourier from his first memoir on the Analytical Theory of Heat to the latest developments in wavelet theory. Originally, Fourier series were used to describe and compute the functions which occur in heat diffusion and equilibrium, but they soon led to the development of new theories by Fourier's followers, and some of these original papers are considered in this text.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 394

Добавлена в каталог: 23.07.2008

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Предметный указатель

"a trous" algorithm      8.1
$C^{\alpha}$ (Hoelder space)      1.5
$H^{1}$ (Hardy space)      6.3
$H^{s}$ (Sobolev space)      1.5
$H_{\epsilon, \epsilon^{'}}$       1.1 2.2
$L^{p}$       6.2
$\phi$ -transform      0.3 2.6
2-microlocalization      0.3 see
Adelson      0.4 0.5 8.2
Admissibility condition      0.2 1.4 7.1
Affine group      0.2 7.1
Almost orthogonal family      1.2 2.2 2.4
Almost wavelets      5.2
Analytic wavelet transform      1.4 8.1
Approximation order      5.2
Arneodo      0.2
Aslaksen      0.2
Asymptotic signals      10.4
Atoms, atomic decomposition      0.3 6.3
Atoms, time-frequency atoms      9.4
Auscher      3.2 3.4 7.2
B-spline      5.3
Baastians      1.3
Balian      1.3
Balian — Low uncertainty theorem      0.3 1.3
Barnwell      0.4
Bases      see "Wavelet bases"
Battle      0.3 1.3 5.2 5.3 7.1
Battle — Lemarie wavelet      0.3 5.2 5.3
BCR algorithm      0.3 8.5
Berkolaiko      5.2
Berkolaiko — Novikov basis      5.2
Besov spaces      0.3 2.6 5.2 6.5 7.3 8.6
Besov spaces, homogeneous      6.5
Best basis      9.2 9.3
Beylkin      0.3 8.4 8.5
Bi-orthogonal wavelets, bi-orthogonal multiresolution analyses      0.5 3.0 3.2 3.3 5.4 6.1
BMO, $BMO_{d}$ , bmo      6.3
Bony      0.3 2.6 6.6 10.1
Bourdaud      6.5
Bourgain      1.3
Box-splines      7.1
Bump element      6.5
Burt      0.4 0.5 8.2
Butterworth scaling filter      5.2
Calderon      0.3 2.6 6.1
Calderon identity      0.3 2.6
Calderon — Zygmund operators      0.3 0.5 6.1 6.4 6.5 8.5 10.1 10.3
Calderon — Zygmund splitting      6.2
Cascade algorithm      5.2 8.4
Chirps      0.3 10.4
Chui      2.1 3.4 5.3
Cohen      4.2 4.3 5.1 5.2 5.4 7.3 8.3
Cohen criterion      4.2 4.4 5.1
Coherent states      0.2
Coiflets      5.2 8.4
Coifman      0.3 0.4 5.2 6.1 6.3 8.4 8.5 9.2 9.3 10.2 10.3
Compression      0.3 0.4 8.6 9.2
Continuous wavelet transform      0.2 8.1 see
Conze      5.1
Correlation function      3.1
Correlation matrix      3.1
Daubechies      0.2 0.3 0.5 1.3 2.1 2.6 4.3 5.1 5.2 5.4 7.3 8.0 8.1 8.3 8.4
Daubechies orthonormal wavelets      0.5 5.2
David      0.5 3.3 10.1 10.3
David — Journe theorem      0.5 10.3
De-noising      8.6
Derivative of a scaling functions      4.2 8.4
Deslauriers      5.1
Dilation matrix      7.1
Discrete wavelet transform      0.1 0.2 2.1 2.5 7.1
Div-curl theorem      10.2
Divergence-free vector fields      7.1
Dobyinsky      10.1 10.2
Donoho      0.3 8.6
Dual frame      1.2 2.5
Dubuc      5.1
Duffin      0.2
Durand      8.4
Dyadic $BMO_{d}$ , dyadic Hardy space $H^{1}_{d}$       6.3
Dyadic cubes      0.3
Dyadic interpolation scheme      5.1
Dyadic martingales      0.3 7.1
Dyn      5.2
Eirola      4.3
entropy      9.2 9.3
Esteban      0.4 8.2
Euler — Frobenius polynomials      5.3
Evangelista      5.2
Evans      10.2
Extremal phase      5.2
Faber      5.2
Farge      0.2
Fast Wavelet Transform      0.4 8.2
Feauveau      0.5 5.4 7.1
Fefferman      6.3
Folded wavelet basis      8.3
Fourier transform      1.1
Fourier windows      0.1 1.3 9.3 9.4
Fractional derivation, integration      2.2 2.5
frames      0.2 1.2 2.1 2.5 7.1
Franklin      5.2
Franklin system      5.2
Frazier      0.3 2.6 6.3
Frisch      0.2 0.5
Functional analysis      0.3 6.1
Fundamental scaling function      4.4
Gabor      0.1 1.3
Gabor wavelets      0.1 1.3
Galand      0.4 8.2
Gaussian functions      0.1 7.1
Gerver      10.4
Goldberg      6.3
Goodman      6.3
Gram operator      1.2
Gripenberg      2.5 6.2
Groechenig      2.1 7.2 7.3
Grossmann      0.2 0.3 2.6
Haar      5.2
Haar basis      0.3 5.2 6.3 7.1 10.3
Half polynomials      8.3
Hardin      9.1
Hardy      10.4
Hardy space, $H^{(2)}$ -analytic      0.2 3.4
Hardy space, $H^{1}$       1.5 6.3 10.1 10.2
Hardy space, $h^{1}$ -local      6.3
Hardy space, $H^{1}_{d}$ -dyadic      6.3
Hardy space, $H^{p}$ , $0<p<+\infty$       0.4 2.6 5.2
Heisenberg Inequality      0.1 1.1
Herley      5.2
Herrmann      0.5
Herve      4.2 4.3 9.1
Hoelder space $C^{\alpha}$       1.5 2.6 7.3 see \infty}_{\infty} \alpha\notin\mathbf{N}$"/>"
Holladay theorem      5.3
Holschneider      1.6 8.1 10.4
Instantaneous frequency      0.1
Interpolating scaling function      5.1
Interpolating scaling function with minimal support      5.1
interval      8.3
Irregular sampling theorem      2.1
Jacobi function $\theta$       10.4
Jaffard      0.3 1.6 6.6 7.1 10.4
Jawerth      0.3 2.6 6.3
Jia      7.2
Johnstone      8.6
Joint resolution      1.4
Jones, L.K.      9.4
Jones, P.      10.3
Jouini      8.3
Journe      0.5 3.3 10.1 10.3

Kessler      9.1
Klauder      0.2
Kronland-Martinet      0.2 8.1
Lacunary Fourier series      1.6
Lagrangian interpolating spline function      5.3
Lam      7.2
Laplacian pyramidal algorithm      0.4 0.5 8.2
Latto      8.4
Lebesgue space $L^{p}$       2.6 5.2 6.2 7.3
Lebesgue space $L^{p}$ , weighted      6.4
Lee      9.1
Lemarie-Rieusset      0.4 3.2 3.4 5.2 5.3 6.4 6.5 7.1 7.2 8.3 8.4
Linear phase      0.5 5.2 5.4
Lions      10.2
Littlewood — Paley decomposition      0.3 2.6
Littlewood — Paley multiresolution analysis      3.3 5.1 5.2
Littlewood — Paley — David wavelet      3.3
Littlewood — Paley — Meyer wavelet      see "Meyer — Lemarie wavelet"
Littlewood — Paley — Stein theory      7.3
Local multiresolution analysis      4.4
Local regularity      6.6
Local sine basis      0.5 9.3
Low      1.6
Lusin area integrals      0.3
Maday      7.1
Madych      7.1 7.3
Malgouyres      4.3 4.4 5.2
Mallat      0.4 3.3 5.2 9.4
Mallat algorithm      0.4 8.0 8.2 9.2
Malvar      0.5 9.3
Malvar window      9.3
Marr      7.1
Massopust      9.1
Matching pursuit algorithm      9.4
Maximally flat filters      0.5
Merging property      9.3
Mexican hat      7.1
Meyer      0.0 0.3 0.4 0.5 1.6 2.2 2.6 3.3 4.4 5.1 5.2 6.1 6.4 6.5 6.6 7.1 7.2 7.3 8.3 9.2 9.3 10.1 10.2 10.4
Meyer — Lemarie wavelet      0.3 0.4 3.3 5.2 6.5 7.2
Micchelli      7.2
Microlocal space $C^{s,s^{'}}_{x_{0}}$       6.6 10.4
Minimal support      4.4
Molecule      6.3 6.5
moment      8.4
Morlet      0.1 0.2 1.4 2.1 8.1
Morlet wavelet      0.1 0.2 1.4 2.1 2.6
Morlet wavelet, multivariate      7.1
Muckenhoupt weights      6.4
Multifractals      0.3 0.5 10.4
Multiresolution analysis      0.4 3.3 4.1 7.1
Multiresolution analysis, $\epsilon$ -localized      4.1
Multiresolution analysis, bi-orthogonal      3.3
Multiresolution analysis, generalized      3.3
Multiresolution analysis, local      4.4
Multiresolution analysis, multiple      9.1
Multiresolution analysis, regular      4.1
Multiscale analysis      0.2
Multivariate wavelets      7
Murenzi      7.1
Non-stationary multiresolution analysis      5.2
Non-stationary signals      9.4
Normalization of a scaling filter      5.2
Novikov      5.2
Orthonormal wavelets, multiresolution analysis, scaling function      0.3 0.5 5.2 8.2 see "Daubechies "Meyer "Stroemberg
Paradifferential operators      0.3 2.6
Paraproducts      10.1
Paul      0.2
Periodic wavelets      8.3
Phase      5.2 5.4
Pittner      0.5
Pointwise regularity      1.6 6.6
Polyharnomic splines      7.1
Polynomial scaling filter      0.5 4.4
Pre-wavelets      5.3
Primitive of a scaling function      4.2 8.4
Projection operators      3.1 3.2 3.4 6.1
Pseudodifferential operators      8.5
Quadrature formulae      8.4
Quadrature mirror filters      0.4 0.5 8.2
Quake      9.2
Quillen — Suslin theorem      7.2
Rational dilation factor      3.2 3.3
Rational filter      5.2
Regular sampling theorem      2.1 7.1
Regularity of the scaling function      4.2 4.3
Reproducing formula      1.2
Resolution      1.1 1.3
Reznikoff      8.4
Ridge and skeleton extraction algorithm      0.2 10.4
Riemann      10.4
Riemann — Weierstrass function      10.4
Riemenschneider      7.1
Riesz basis      1.2
Riesz lemma      0.5 5.2
Rioul      5.2
Rokhlin      0.3 8.4 8.5
RON      5.2
Rvachev function      5.2
Scaling filter      0.4 4.1 4.2
Scaling function      0.4 4.1
Scaling function, $\epsilon$ -localized      4.1
Scaling function, compactly supported      4.4
Scaling function, fundamental      4.4
Scaling function, interpolating      5.1
Scaling function, regular      4.1
Schaeffer      0.2
Schauder      5.2
Schneid      0.5
Schoenberg      5.3
Self-similar tilings      7.3
Semmes      10.2 10.3
Separable wavelets      7.1
Separation lemma      4.4
Shen      7.1
Shi      2.1 3.4
Shift-invariant spaces      3.1 7.2
Short wavelets      9.1
Short-Time Fourier Transform      0.1 see
smith      0.4
Sobolev spaces $H^{s}$       1.5 2.5 2.6 5.2 7.3 see 2}_{2}$"/>"
Spline Function      5.3
Spline function with multiple knots      9.1
Spline wavelets      0.4 5.2 5.3 5.4
Stegers      1.6
Stein      0.3 6.1 6.3 7.3
Strang — Fix conditions      0.5 5.2
Stroemberg      0.4 5.2 5.3
Stroemberg spline wavelet      5.2 5.3
Subband coding scheme      0.4 8.2 9.2
Sweldens      8.4
Symmetric scaling function      8.3
Tabulation of a scaling function      8.4
Tang      9.1
Tchamitchian      0.2 1.6 10.4
Tenenbaum      8.4
Tensor product of multiresolution analyses      7.1
Tight frame      1.2
Time-frequency analysis      0.1
Time-frequency atoms      9.4
Torresani      0.2 10.4
Transition operator      4.2 4.3 4.4 5.1
Turbulence      0.2
Two-scale difference equation      4.1 8.4
Ueberhuber      0.5
Unconditional basis      6.1
Vaguelettes lemma      2.2 7.1
Vetterli      5.2
Vial      8.3
Ville      0.1
Villemoes      4.3 7.3

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