21 citations · 36 across the 10 of their papers we have counts for
11 papers
Spherical Basis Functions in Hardy Spaces with Localization Constraints
Christian Gerhards, Xinpeng Huang
Subspaces obtained by the orthogonal projection of locally supported square-integrable vector fields onto the Hardy spaces and , respectively, pl…
Relation between Hardy components for locally supported vector fields on the sphere
Christian Gerhards, Xinpeng Huang, Alexander Kegeles
Given a function in the Hardy space of inner harmonic gradients on the sphere, H+(S), we consider the problem of finding a corresponding function in the Hardy space of outer harmon…
Unique reconstruction of simple magnetizations from their magnetic potential
L. Baratchart, C. Gerhards, A. Kegeles +1
Inverse problems arising in (geo)magnetism are typically ill-posed, in particular {they exhibit non-uniqueness}. Nevertheless, there exist nontrivial model spaces on which the prob…
Decomposition of -vector fields on Lipschitz surfaces: characterization via null-spaces of the scalar potential
L. Baratchart, C. Gerhards, A. Kegeles
For the boundary of a bounded and connected strongly Lipschitz domain in with , we prove that any field $f\in L^{2} (\partial Ω; \mathbb{R}^{d…
On the Recovery of Core and Crustal Components of Geomagnetic Potential Fields
Laurent Baratchart, Christian Gerhards
In Geomagnetism it is of interest to separate the Earth's core magnetic field from the crustal magnetic field. However, measurements by satellites can only sense the sum of the two…
On the Reconstruction of Dipole Directions from Spherical Magnetic Field Measurements
Christian Gerhards
Reconstructing magnetizations from measurements of the generated magnetic potential is generally non-unique. The non-uniqueness still remains if one restricts the magnetization to…
Spherical Potential Theory: Tools and Applications
Christian Gerhards
This paper provides an overview on tools from potential theory on the sphere and some applications in geoscience.
A Parameter Choice Strategy for the Inversion of Multiple Observations
C. Gerhards, S. Pereverzyev, P. Tkachenko
In many geoscientific applications, multiple noisy observations of different origin need to be combined to improve the reconstruction of a common underlying quantity. This naturall…
On the Unique Reconstruction of Induced Spherical Magnetizations
Christian Gerhards
Recovering spherical magnetizations from magnetic field data in the exterior is a highly non-unique problem. A spherical Hardy-Hodge decomposition supplies information on what…
Locally Supported Wavelets for the Separation of Spherical Vector Fields with Respect to their Sources
Christian Gerhards
We provide a space domain oriented separation of magnetic fields into parts generated by sources in the exterior and sources in the interior of a given sphere. The separation itsel…
A Combination of Downward Continuation and Local Approximation for Harmonic Potentials
Christian Gerhards
This paper presents a method for the approximation of harmonic potentials that combines downward continuation of globally available data on a sphere of radius (e.g., a sa…