Decomposition of Besov and Triebel–Lizorkin spaces on the sphere

By Francis J. Narcowich, Pencho Petrushev, Joseph D. Ward. 2006

176 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f07114b98de6ced3e454a3adf37df3006f1f9e25

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Continuous wavelets on compact manifolds (2008, methodology): “Most relevantly, in 2006 Narcowich, Petrushev and Ward ([35], [36]) showed a slight variant of Lemma 4.”
A class of Laplacian multiwavelets bases for high-dimensional data (2015, unknown): “From [34], for any 0 < α ≤ s and a, b > 0 we have aαbs−α ≤ (a + b) .”
Localized Tight Frames on Spheres (2006, methodology): “In particular, they can be used in the construction and characterization of many of the classical Banach spaces, including L(S), Besov spaces, and Triebel–Lizorkin spaces [18].”
Localized Polynomial Frames on the Ball (2006, unknown): “Then for every k > 0 and r ≥ 0 there exists a constant ck > 0 depending only on k, r, α, β, and â such that (3.6) ∣∣∣ d r dxr Lα,βn (cos θ) ∣∣∣ ≤ ck n2α+2r+2 (1 + nθ)k , 0 ≤ θ ≤ π.”
Decomposition of Spaces of Distributions Induced by Hermite Expansions (2007, unknown): “Our main results assert that the Hermite-Triebel-Lizorkin and Hermite Besov spaces can be characterized in terms of respective sequence norms of the needlet coefficients of the distributions (Theorems 4.5, 5.7).”
Heat Kernel Generated Frames in the Setting of Dirichlet Spaces (2012, background): “We would like to point out that the case of the sphere endowed with the natural Laplace-Beltrami operator treated in [42, 43] and the case of more general compact homogeneous spaces endowed with the Casimir operator considered in [24] fall into the above category.”
Nearly tight frames and space-frequency analysis on compact manifolds (2007, methodology): “Independently of us, Narcowich, Petrushev and Ward ([31], [32]) have developed systems of tight frames for S which are related to the frames of this article; they have been dubbed “needlets”, and used by astrophysicists to study cosmic microwave background radiation.”
Irregular sampling of band-limited functions on the sphere (2014, unknown): “The idea of using spherical needlets for sampling of high degree spherical polynomials is rooted in the highly localized kernels, developed in [13,14], where they are used for the construction of frames on the sphere (termed also needlets).”