# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# educationAndTraining[].organization.label
Princeton University - (Princeton, New Jersey, United States)

# educationAndTraining[].organization.label
Princeton University - (Princeton, New Jersey, United States)

# awardsAndHonors[].label
Association of Former Students College-Level Teaching Distinguished Achievement Award, The

# publications[].label
A First Course in Wavelets with Fourier Analysis

# publications[].label
KERNEL APPROXIMATION ON MANIFOLDS II: THE L-infinity NORM OF THE L-2 PROJECTOR

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Corrigendum to "Spherical Marcinkiewicz-Zygmund inequalties and positive quadrature" (vol 70, pg 1113, 2001)

# publications[].label
Quasi-interpolation in shift invariant spaces

# publications[].label
Kernel Approximation on Manifolds II: The $L_{infty}$-norm of the  $L_2$-projector

# publications[].label
Forty More Years of Ramifications Spectral Asymptotics and Its Applications

# publications[].label
EXTREME POINTS OF INTERVAL BETWEEN 2 OPERATORS

# publications[].label
A Meshless Galerkin Method For Non-Local Diffusion Using Localized  Kernel Bases

# publications[].label
On the representation of band-dominant functions of the sphere using finitely many bits (vol 21, pg 127, 2004)

# publications[].label
Kernel Based Quadrature on Spheres and Other Homogeneous Spaces

# publications[].label
Decomposition of Besov and TriebelLizorkin spaces on the sphere

# publications[].label
ON CONDITION NUMBERS ASSOCIATED WITH RADIAL-FUNCTION INTERPOLATION

# publications[].label
LeVeque type inequalities and discrepancy estimates for minimal energy configurations on spheres

# publications[].label
Direct and inverse Sobolev error estimates for scattered data interpolation via spherical basis functions

# publications[].label
A first course in wavelets with fourier analysis

# publications[].label
Direct and Inverse Results on Bounded Domains for Meshless Methods via Localized Bases on Manifolds

# publications[].label
Sobolev error estimates and a Bernstein inequality for scattered data interpolation via radial basis functions

# publications[].label
THE PROBLEM OF MOMENTS IN THE PHASE-SPACE FORMULATION OF QUANTUM-MECHANICS

# publications[].label
Zonal function network frames on the sphere.

# publications[].label
Nonstationary wavelets on the m-sphere for scattered data

# publications[].label
A First Course in Wavelets with Fourier Analysis

# publications[].label
Sufficient conditions for penalty formulation methods in analytical dynamics

# publications[].label
Polyharmonic and Related Kernels on Manifolds: Interpolation and  Approximation

# publications[].label
L-p BERNSTEIN ESTIMATES AND APPROXIMATION BY SPHERICAL BASIS FUNCTIONS

# publications[].label
IMBEDDING THEOREM FOR INDETERMINATE HERMITIAN MOMENT SEQUENCES

# publications[].label
Approximation power of RBFs and their associated SBFs: a connection

# publications[].label
Norms of Inverses for Matrices Associated with Scattered Data

# publications[].label
On the representation of band-dominant functions on the sphere using finitely many bits

# publications[].label
Locally supported, quasi-interpolatory bases on graphs

# publications[].label
Recent developments in error estimates for scattered-data interpolation via radial basis functions

# publications[].label
APPROXIMATION OF POINCARE SECTIONS ARISING IN ATTITUDE-CONTROL

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
GENERALIZED HERMITE INTERPOLATION AND POSITIVE-DEFINITE KERNELS ON A RIEMANNIAN MANIFOLD

# publications[].label
DISTRIBUTIONS OF H-POSITIVE TYPE AND APPLICATIONS

# publications[].label
PERSISTENCY OF EXCITATION, IDENTIFICATION, AND RADIAL BASIS FUNCTIONS

# publications[].label
An inverse theorem for compact Lipschitz regions in d using localized kernel bases.

# publications[].label
L^p Bernstein estimates and approximation by spherical basis functions

# publications[].label
A NOVEL GALERKIN METHOD FOR SOLVING PDES ON THE SPHERE USING HIGHLY LOCALIZED KERNEL BASES

# publications[].label
Pad approximation and gaussian quadrature

# publications[].label
SUPPORT FUNCTIONS FOR MATRIX RANGES - ANALOGS OF LUMER FORMULA

# publications[].label
A high-order meshless Galerkin method for semilinear parabolic equations on spheres

# publications[].label
OPERATOR VERSION OF A THEOREM OF KOLMOGOROV

# publications[].label
Meshfree Extrapolation with Application to Enhanced Near-Boundary Approximation with Local Lagrange Kernels

# publications[].label
Scattered data interpolation on spheres: Error estimates and locally supported basis functions

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Interpolating splines on graphs for data science applications

# publications[].label
Variational principles and Sobolev-type estimates for generalized interpolation on a Riemannian manifold

# publications[].label
A MESHLESS GALERKIN METHOD FOR NON-LOCAL DIFFUSION USING LOCALIZED KERNEL BASES

# publications[].label
Highly Localized RBF Lagrange Functions for Finite Difference Methods on  Spheres

# publications[].label
A meshless Galerkin method for non-local diffusion using localized kernel bases.

# publications[].label
Cardinal Interpolation with Gaussian Kernels

# publications[].label
Continuous and discrete least-squares approximation by radial basis functions on spheres

# publications[].label
Scattered-data interpolation on R-n: Error estimates for radial basis and band-limited functions

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
A DYSON-LIKE EXPANSION FOR SOLUTIONS TO THE QUANTUM LIOUVILLE EQUATION

# publications[].label
Mathematical theory of the R matrix. I. The eigenvalue problem

# publications[].label
Necessary and sufficient conditions for a phase-space function to be a Wigner distribution.

# publications[].label
NORM ESTIMATES FOR THE INVERSES OF A GENERAL-CLASS OF SCATTERED-DATA RADIAL-FUNCTION INTERPOLATION MATRICES

# publications[].label
Collocation discretizations of the transport equation with radial basis functions

# publications[].label
NORMS OF INVERSES AND CONDITION NUMBERS FOR MATRICES ASSOCIATED WITH SCATTERED DATA

# publications[].label
On the representation of band-dominant functions on the sphere using finitely many bits

# publications[].label
LOCALIZED BASES FOR KERNEL SPACES ON THE UNIT SPHERE

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
The mathematical theory of the R matrix. II. The R matrix and its properties

# publications[].label
KERNEL APPROXIMATION ON MANIFOLDS I: BOUNDING THE LEBESGUE CONSTANT

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Direct and Inverse Results on Bounded Domains for Meshless Methods via  Localized Bases on Manifolds

# publications[].label
AN ASYMPTOTIC AVERAGE DECAY-RATE FOR THE WAVE-EQUATION WITH VARIABLE-COEFFICIENT VISCOUS DAMPING

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
REPRESENTATION AND APPROXIMATION OF A CLASS OF OPERATOR-VALUED ANALYTIC-FUNCTIONS

# publications[].label
Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting

# publications[].label
Pad approximation and orthogonal polynomials

# publications[].label
EXPONENTIAL DECAY OF ENERGY OF EVOLUTION-EQUATIONS WITH LOCALLY DISTRIBUTED DAMPING

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
An inverse theorem for compact Lipschitz regions in $R^d$ using  localized kernel bases

# publications[].label
Localized bases for kernel spaces on the unit sphere

# publications[].label
A BASIS FOR THE LOCAL SOLUTIONS OF AN ELLIPTIC EQUATION

# publications[].label
Approximation in Sobolev spaces by kernel expansions

# publications[].label
Polyharmonic and Related Kernels on Manifolds: Interpolation and Approximation

# publications[].label
Erratum: 'On the representation of band-dominant functions of the sphere using finitely many bits' (Advances in Computational Mathematics (2004) 21 (127-146))

# publications[].label
Kernel Approximation on Manifolds I: Bounding the Lebesgue Constant

# publications[].label
ANALYTIC PROPERTIES OF THE BOUNDARY OF THE NUMERICAL RANGE

# publications[].label
Wavelets associated with periodic basis functions

# publications[].label
AN INVERSE THEOREM FOR COMPACT LIPSCHITZ REGIONS IN R-d USING LOCALIZED KERNEL BASES

# publications[].label
Kernel based quadrature on spheres and other homogeneous spaces

# publications[].label
Approximation properties of zonal function networks using scattered data on the sphere

# publications[].label
A UNIFIED APPROACH TO QUANTUM DYNAMICAL MAPS AND GAUSSIAN WIGNER DISTRIBUTIONS

# publications[].label
Locally supported, quasi-interpolatory bases on graphs

# publications[].label
On the representation of band-dominant functions on the sphere using finitely many bits (vol 21, pg 127, 2004)

# publications[].label
Interpolating splines on graphs for data science applications

# publications[].label
Cardinal Interpolation with Gaussian Kernels

# publications[].label
A First Course in Wavelets with Fourier Analysis

# publications[].label
Generalized Hermite interpolation via matrix-valued conditionally positive definite functions

# publications[].label
CONVERGENCE OF DIAGONAL OPERATOR-VALUED PADE APPROXIMANTS TO DYSON EXPANSION

# publications[].label
CONDITIONS FOR THE CONVOLUTION OF 2 WIGNER DISTRIBUTIONS TO BE ITSELF A WIGNER DISTRIBUTION

# publications[].label
SINGULARITY STRUCTURE OF THE 2-POINT FUNCTION IN QUANTUM-FIELD THEORY IN CURVED SPACETIME .2.

# publications[].label
R-OPERATORS .1. REPRESENTATION THEORY AND APPLICATIONS

# publications[].label
A Novel Galerkin Method for Solving PDEs on the Sphere Using Highly  Localized Kernel Bases

# publications[].label
Advances in Computational Mathematics: Preface

# publications[].label
R-OPERATORS-II - APPROXIMATION OF CERTAIN OPERATOR-VALUED ANALYTIC-FUNCTIONS AND HERMITIAN MOMENT PROBLEM

# publications[].label
Refined error estimates for radial basis function interpolation

# publications[].label
A TOEPLITZ-HAUSDORFF THEOREM FOR MATRIX RANGES

# publications[].label
ERROR AND STABILITY ESTIMATES FOR SURFACE-DIVERGENCE FREE RBF INTERPOLANTS ON THE SPHERE

# publications[].label
Stability results for scattered-data interpolation on Euclidean spheres

# publications[].label
PERSISTENCY OF EXCITATION IN IDENTIFICATION USING RADIAL BASIS FUNCTION APPROXIMANTS

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
A CHARACTERIZATION OF ESSENTIAL MATRIX RANGES

# researcherOn[].label
Localized Kernel Bases: Theory and Applications to Meshless Methods

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
Localized Kernel Bases With Application To Meshless Methods

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
Theory and Applications of Localized Kernel Bases to Meshfree Methods

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# streetAddress
Texas A&M University; Mathematics; 3368 TAMU

# etdChairOf[].label
Fuselier, Edward J., Jr. (2007-09). Refined error estimates for matrix-valued radial basis functions. Doctoral Dissertation.

# etdChairOf[].label
Ward, John P. (2012-10). L^p Bernstein Inequalities and Radial Basis Function Approximation. Doctoral Dissertation.

# etdChairOf[].label
Lowitzsch, Svenja (2004-09). Approximation and interpolation employing divergence-free radial basis functions with applications. Doctoral Dissertation.

# etdChairOf[].label
Le Gia, Quoc Thong (2004-09). Approximation of linear partial differential equations on spheres. Doctoral Dissertation.

# etdChairOf[].label
Rowe, Stephen Taber (2015-04). Meshfree Methods Using Localized Kernel Bases. Doctoral Dissertation.