227 citations
- University of BirminghamGB9 papers
- University of Maryland, College ParkUS8 papers
- Rutherford Appleton LaboratoryGB7 papers
- California Institute of TechnologyUS6 papers
- Columbia UniversityUS6 papers
- East China Normal UniversityCN6 papers
- Stanford UniversityUS6 papers
- University of FloridaUS6 papers
- University of WashingtonUS6 papers
- European Organization for Nuclear ResearchCH5 papers
- Louisiana State UniversityUS5 papers
- Max Planck Institute for Gravitational PhysicsDE5 papers
17 papers · 1 filter
Sub-exponentially localized kernels and frames induced by orthogonal expansions
Kamen Ivanov, Pencho Petrushev, Yuan Xu
The aim of this paper is to construct sup-exponentially localized kernels and frames in the context of classical orthogonal expansions, namely, expansions in Jacobi polynomials, sp…
Decomposition of Triebel-Lizorkin and Besov spaces in the context of Laguerre expansions
G. Kerkyacharian, P. Petrushev, D. Picard +1
A pair of dual frames with almost exponentially localized elements (needlets) are constructed on $\RR_+^d$ based on Laguerre functions. It is shown that the Triebel-Lizorkin and Be…
Fourier series and approximation on hexagonal and triangular domains
Yuan Xu
Several problems on Fourier series and trigonometric approximation on a hexagon and a triangle are studied. The results include Abel and Cesàro summability of Fourier series, degre…
Krall--type Orthogonal Polynomials in several variables
Lidia Fernandez, Teresa E. Perez, Miguel A. Pinar +1
For a bilinear form obtained by adding a Dirac mass to a positive definite moment functional in several variables, explicit formulas of orthogonal polynomials are derived from the…
Orthogonal polynomials and partial differential equations on the unit ball
Miguel Pinar, Yuan Xu
Orthogonal polynomials of degree with respect to the weight function on the unit ball in $\RR^d$ are known to satisfy the partial differential equation…
Decomposition of spaces of distributions induced by Hermite expansions
Pencho Petrushev, Yuan Xu
Decomposition systems with rapidly decaying elements (needlets) based on Hermite functions are introduced and explored. It is proved that the Triebel-Lizorkin and Besov spaces on $…