Lectures on constructive approximation. Fourier, spline, and wavelet methods on the real line, the sphere, and the ball

DOI10.1007/978-0-8176-8403-7zbMath1295.65003OpenAlexW2481653444MaRDI QIDQ1761413

Volker Michel

Publication date: 15 November 2012

Published in: Applied and Numerical Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-0-8176-8403-7

zbMATH Keywords

waveletssplinestextbookspherical harmonicsFourier seriesspherical approximationconstructive approximation

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Numerical methods for wavelets (65T60) Numerical methods for trigonometric approximation and interpolation (65T40) Spherical harmonics (33C55) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis (65-01)

Related Items (36)

New type of Gegenbauer-Jacobi-Hermite monogenic polynomials and associated continuous Clifford wavelet transform. Some monogenic Clifford polynomials and associated wavelets ⋮ Approximation properties of the double Fourier sphere method ⋮ Funk-Minkowski transform and spherical convolution of Hilbert type in reconstructing functions on the sphere ⋮ Reconstructing a function on the sphere from its means along vertical slices ⋮ An SVD in Spherical Surface Wave Tomography ⋮ Some old orthogonal polynomials revisited and associated wavelets: two-parameters Clifford-Jacobi polynomials and associated spheroidal wavelets ⋮ Symbolic abstractions for nonlinear control systems via feedback refinement relation ⋮ A unified approach to scalar, vector, and tensor Slepian functions on the sphere and their construction by a commuting operator ⋮ Vector-valued spline method for the spherical multiple-shell electro-magnetoencephalography problem ⋮ A double Fourier sphere method for \(d\)-dimensional manifolds ⋮ Uncertainty principle and phase-amplitude analysis of signals on the unit sphere ⋮ Sliced optimal transport on the sphere ⋮ Some ultraspheroidal monogenic Clifford Gegenbauer Jacobi polynomials and associated wavelets ⋮ The Funk-Radon transform for hyperplane sections through a common point ⋮ A non-linear approximation method on the sphere ⋮ Vectorial Slepian Functions on the Ball ⋮ SPHARMA approximations for stationary functional time series on the sphere ⋮ Optical flow on evolving sphere-like surfaces ⋮ A greedy algorithm for nonlinear inverse problems with an application to nonlinear inverse gravimetry ⋮ Decomposition of optical flow on the sphere ⋮ Smooth orthogonal projections on sphere ⋮ The Regularized Orthogonal Functional Matching Pursuit for Ill-Posed Inverse Problems ⋮ Functional penalised basis pursuit on spheres ⋮ Theory of generalized discrepancies on a ball of arbitrary finite dimensions and algorithms for finding low-discrepancy point sets ⋮ On the null space of a class of Fredholm integral equations of the first kind ⋮ A first approach to learning a best basis for gravitational field modelling ⋮ New type of Gegenbauer-Hermite monogenic polynomials and associated Clifford wavelets ⋮ A Numerical Framework for Efficient Motion Estimation on Evolving Sphere-Like Surfaces Based on Brightness and Mass Conservation Laws ⋮ Convolutions on the sphere: commutation with differential operators ⋮ Fast cross-validation in harmonic approximation ⋮ Singular value decomposition of the longitudinal ray transform of vector fields in a ball in cone beam coordinates ⋮ Parameter Choices for Fast Harmonic Spline Approximation ⋮ Spherical Harmonics Based Special Function Systems and Constructive Approximation Methods ⋮ On the Non-uniqueness of Gravitational and Magnetic Field Data Inversion (Survey Article) ⋮ Regularized functional matching pursuit for the spherical multiple-shell electro-magnetoencephalography problem ⋮ Approximating the derivative of manifold-valued functions

This page was built for publication: Lectures on constructive approximation. Fourier, spline, and wavelet methods on the real line, the sphere, and the ball