Representation of Fourier integral operators using shearlets

DOI10.1007/s00041-008-9018-0zbMath1213.42109OpenAlexW2014172718MaRDI QIDQ929332

Kanghui Guo, Demetrio Labate

Publication date: 17 June 2008

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-008-9018-0

zbMATH Keywords

waveletsFourier integral operatorssparsitycurveletspseudo differential operators

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) General harmonic expansions, frames (42C15)

Related Items (22)

SHEARLET TRANSFORMS AND DIRECTIONAL REGULARITIES ⋮ \(\alpha\)-Molecules ⋮ Efficient Analysis and Detection of Edges Through Directional Multiscale Representations ⋮ Parabolic Molecules: Curvelets, Shearlets, and Beyond ⋮ Parabolic molecules ⋮ Computing Fourier integral operators with caustics ⋮ Efficient representation of spatio-temporal data using cylindrical shearlets ⋮ Tree approximation with anisotropic decompositions ⋮ Multivariate \(\alpha\)-molecules ⋮ Shearlet smoothness spaces ⋮ Triebel-Lizorkin spaces and shearlets on the cone in \(\mathbb R^2\) ⋮ Intrinsic localization of anisotropic frames ⋮ Approximation of Fourier integral operators by Gabor multipliers ⋮ Almost diagonalization of \(\tau \)-pseudodifferential operators with symbols in Wiener amalgam and modulation spaces ⋮ Intrinsic localization of anisotropic frames. II: \(\alpha\)-molecules ⋮ Schatten class Fourier integral operators ⋮ Estimations of directional Hölder regularity by shearlets ⋮ Smooth projections and the construction of smooth Parseval frames of shearlets ⋮ Almost Diagonalization of Pseudodifferential Operators ⋮ Frame properties of generalized shift-invariant systems in discrete setting ⋮ An extension of shearlet-based Triebel-Lizorkin spaces and BMO ⋮ SHEAR ANISOTROPIC INHOMOGENEOUS BESOV SPACES IN ℝ^d

Cites Work

• Asymptotic solutions of oscillatory initial value problems
• Sparse directional image representations using the discrete shearlet transform
• A parametrix construction for wave equations with \(C^{1,1}\) coefficients
• A Hardy space for Fourier integral operators
• The art of frame theory
• Foundations of time-frequency analysis
• Wavelets with composite dilations and their MRA properties
• Fast wavelet transforms and numerical algorithms I
• THE UNCERTAINTY PRINCIPLE ASSOCIATED WITH THE CONTINUOUS SHEARLET TRANSFORM
• Resolution of the wavefront set using continuous shearlets
• New tight frames of curvelets and optimal representations of objects with piecewise C² singularities
• Wavelets with composite dilations
• Optimally Sparse Multidimensional Representation Using Shearlets
• The curvelet representation of wave propagators is optimally sparse
• An introduction to frames and Riesz bases
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