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We consider the problem of approximately reconstructing a function f defined on the surface of the unit sphere in the Euclidean space R, using samples of f at scattered sites. A central role is… (More)

Let {φk} be an orthonormal system on a quasi-metric measure space X, {`k} be a nondecreasing sequence of numbers with limk→∞ `k = ∞. A diffusion polynomial of degree L is an element of the span of… (More)

- Frank Filbir, Hrushikesh Narhar Mhaskar
- J. Complexity
- 2011

Let X be a compact, connected, Riemannian manifold (without boundary), ρ be the geodesic distance on X, μ be a probability measure on X, and {φk} be an orthonormal (with respect to μ) system of… (More)

- Edwin van Beek, Joerg Schmiedeskamp, +10 authors Egbert Otten
- European Radiology
- 2003

The aim of this study was to test the feasibility of a central production facility with distribution network for implementation of hyperpolarized 3-helium MRI. The 3-helium was hyperpolarized to… (More)

Starting from a natural generalization of the trigonometric case, we construct a de la Vallée Poussin approximation process in the uniform and L norms. With respect to the classical approach we… (More)

- Wolfgang zu Castell, Frank Filbir
- Journal of Approximation Theory
- 2005

Since radial positive definite functions on R remain positive definite when restricted to the sphere, it is natural to ask for properties of the zonal series expansion of such functions which relate… (More)

- Martin Ehler, Frank Filbir, Hrushikesh Narhar Mhaskar
- Journal of Computational Biology
- 2012

Diffusion geometry techniques are useful to classify patterns and visualize high-dimensional datasets. Building upon ideas from diffusion geometry, we outline our mathematical foundations for… (More)

- Frank Filbir, Dominik Schmid
- Journal of Approximation Theory
- 2008

- Frank Filbir, Stefan Kunis, Ruben Seyfried
- SIAM J. Numerical Analysis
- 2014

where Sd−1 = { u ∈ Rd : |u| = 1 } denotes the unit sphere and σ its surface measure. In particular is σ(S1) = 2π and σ(S2) = 4π. The variable t ≥ 0 is called measurement time and the variable ξ ∈ Rd… (More)

- Sabine Eisenhofer, Ferenc Toókos, Burkhard A. Hense, Sabine Marita Schulz, Frank Filbir, Hans Zischka
- BMC Research Notes
- 2010

The permeabilization of mitochondrial membranes is a decisive event in apoptosis or necrosis culminating in cell death. One fundamental mechanism by which such permeabilization events occur is the… (More)