What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Quantum mechanics
- Algebra
Francis J. Narcowich focuses on Mathematical analysis, Radial basis function, Positive-definite matrix, Spherical harmonics and Sobolev space.
His work on Bounded function, Pointwise and Self-adjoint operator as part of his general Mathematical analysis study is frequently connected to n-sphere and SPHERES, thereby bridging the divide between different branches of science.
The Positive-definite matrix study combines topics in areas such as Condition number, Inverse and Combinatorics.
In his study, which falls under the umbrella issue of Spherical harmonics, Numerical integration, Eigenfunction, Harmonic function and Legendre polynomials is strongly linked to Unit sphere.
His Sobolev space research is multidisciplinary, incorporating perspectives in Reproducing kernel Hilbert space, Hilbert space, Lipschitz domain, Function and Least squares.
His Hilbert space course of study focuses on Interpolation and Discrete mathematics, Linear combination and Norm.
His most cited work include:
- Localized Tight Frames on Spheres (277 citations)
- Persistency of Excitation in Identification Using Radial Basis Function Approximants (185 citations)
- Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature (180 citations)
What are the main themes of his work throughout his whole career to date?
Francis J. Narcowich mainly focuses on Mathematical analysis, Pure mathematics, Interpolation, Sobolev space and Radial basis function.
His Mathematical analysis research is multidisciplinary, relying on both Positive-definite matrix and Surface.
Francis J. Narcowich has researched Pure mathematics in several fields, including Norm, Bounded function and Inverse.
His studies deal with areas such as Space, Gaussian, Fourier transform and Basis as well as Interpolation.
His studies in Sobolev space integrate themes in fields like Smoothness, Type, Least squares and Bernstein inequalities.
His Unit sphere study incorporates themes from Function, Numerical integration, Euclidean space and Spherical harmonics.
He most often published in these fields:
- Mathematical analysis (50.00%)
- Pure mathematics (27.55%)
- Interpolation (19.39%)
What were the highlights of his more recent work (between 2008-2021)?
- Pure mathematics (27.55%)
- Mathematical analysis (50.00%)
- Sobolev space (19.39%)
In recent papers he was focusing on the following fields of study:
His primary areas of investigation include Pure mathematics, Mathematical analysis, Sobolev space, Bounded function and Applied mathematics.
His Pure mathematics research is multidisciplinary, incorporating elements of Positive-definite matrix, Norm, Kernel approximation and Inverse.
His work on Spherical harmonics is typically connected to Stiffness matrix as part of general Mathematical analysis study, connecting several disciplines of science.
His research investigates the connection with Sobolev space and areas like Linear combination which intersect with concerns in Combinatorics, Dimension, Basis function, Power function and Type.
His Bounded function research includes elements of Surface, Lipschitz continuity and Lebesgue integration.
His Applied mathematics research incorporates themes from Function, Discretization, Numerical analysis and Galerkin method.
Between 2008 and 2021, his most popular works were:
- L p Bernstein Estimates and Approximation by Spherical Basis Functions (48 citations)
- Kernel Approximation on Manifolds I: Bounding the Lebesgue Constant (44 citations)
- Localized Bases for Kernel Spaces on the Unit Sphere (31 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Quantum mechanics
- Algebra
His primary scientific interests are in Pure mathematics, Sobolev space, Mathematical analysis, Manifold and Interpolation.
Francis J. Narcowich specializes in Pure mathematics, namely Unit sphere.
The various areas that Francis J. Narcowich examines in his Sobolev space study include Bernstein polynomial, Norm and Bounded function.
Francis J. Narcowich focuses mostly in the field of Mathematical analysis, narrowing it down to matters related to Positive-definite matrix and, in some cases, Numerical integration and Rotation group SO.
Francis J. Narcowich studied Manifold and Lebesgue integration that intersect with Riemannian manifold, Constant and Center.
His work deals with themes such as Geometry, Surface and Numerical stability, which intersect with Interpolation.
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