Localized Tight Frames on Spheres

By Francis J. Narcowich, Pencho Petrushev, Joseph D. Ward. SIAM Journal on Mathematical Analysis, 2006

325 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c0e9e15b3468a445991d9cf6f22ee829a1fa9039

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

1. Azita Mayeli
2. Daryl Geller
3. Pencho Petrushev
4. Gerard Kerkyacharian
5. Yuan Xu
6. T. Coulhon
7. Dominique Picard
8. Francis J. Narcowich

In Mathematical Physics

1. Daryl Geller
2. Azita Mayeli
3. Pencho Petrushev
4. Yuan Xu
5. Gerard Kerkyacharian
6. T. Coulhon
7. Dominique Picard
8. Francis J. Narcowich

Citations in the corpus

• Spherical needlets for cosmic microwave background data analysis (2008, background): “3 P RO P E RT I E S A N D C O M PA R I S O N S The following quasi-exponential localization property of needlets is due to Narcowich et al. (2006) and motivates their name.”
• Localized Polynomial Frames on the Interval with Jacobi Weights (2005, methodology): “This result is a far reaching extension of the recent discovery in [7] that L n (x, 1) (with λ a half integer) has almost exponential localization around x = 1, which is utilized in [7] for the construction of frames on the n dimensional sphere.”
• Heat Kernel Generated Frames in the Setting of Dirichlet Spaces (2012, methodology): “This simple fact has been utilized for construction of frames on the sphere [42], on the interval with Jacobi weights [47], on the ball [48], and in the context of Hermite [49] and Laguerre [34] expansions.”
• 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).”
• Wavelet transform on manifolds: Old and new approaches (2010, background): “This idea, originally due to Holschneider [18] and Freeden [14], has been revived in the context of spherical wavelets [21, 30, 32] and the so-called needlets [22].”
• Continuous wavelets on compact manifolds (2008, methodology): “Narcowich, Petrushev and Ward do not discuss continuous wavelets, but use spectral theory arguments to construct tight frames on Sn.”
• 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.”
• Localized Polynomial Frames on the Ball (2006, background): “This relation leads us to the following distance on Bd, which will play a vital role in the following: (4.6) d(x, y) := arccos { 〈x, y〉+ √ 1− |x|2 √ 1− |y|2 } .”
• Asymptotics for spherical needlets (2006, background): “See also Nualart and Peccati (2005) for a more recent point of view.”
• Decomposition of Besov and Triebel–Lizorkin spaces on the sphere (2006, background): “[11] Letâ be admissible.”
• A full sky, low foreground, high resolution CMB map from WMAP (2008, background): “Needlets were introduced by Narcowich et al. (2006) as a particular construction of a wavelet frame on the sphere.”