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1.
Stephan Dahlke Gabriele Steidl Gerd Teschke 《Journal of Fourier Analysis and Applications》2004,10(5):507-539
This article is concerned with frame constructions on domains and manifolds. The
starting point is a unitary group representation which is square integrable modulo a suitable
subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized
coorbit spaces can be defined by collecting all functions for which this wavelet transform
is contained in a weighted Lp-space. Moreover, we show that a judicious discretization of the
representation leads to an atomic decomposition and to Banach frames for these coorbit spaces. 相似文献
2.
Arne Barinka Stephan Dahlke Wolfgang Dahmen 《Advances in Computational Mathematics》2006,24(1-4):5-34
Recently adaptive wavelet methods have been developed which can be shown to exhibit an asymptotically optimal accuracy/work
balance for a wide class of variational problems including classical elliptic boundary value problems, boundary integral equations
as well as certain classes of noncoercive problems such as saddle point problems. A core ingredient of these schemes is the
approximate application of the involved operators in standard wavelet representation. Optimal computational complexity could
be shown under the assumption that the entries in properly compressed standard representations are known or computable in
average at unit cost. In this paper we propose concrete computational strategies and show under which circumstances this assumption
is justified in the context of elliptic boundary value problems.
Dedicated to Charles A. Micchelli on the occasion of his 60th birthday
Mathematics subject classifications (2000) 41A25, 41A46, 65F99, 65N12, 65N55.
This work has been supported in part by the Deutsche Forschungsgemeinschaft SFB 401, the first and third author are supported
in part by the European Community's Human Potential Programme under contract HPRN-CT-202-00286 (BREAKING COMPLEXITY). The
second author acknowledges the financial support provided through the European Union's Human Potential Programme, under contract
HPRN-CT-2002-00285 (HASSIP) and through DFG grant DA 360/4–1. 相似文献
3.
Structural and Magnetochemical Studies on KCuGaF6 The crystal structure of KCuGaF6 was determined on the base of X‐ray single crystal data (wR2 = 0.084 for 2476 independent reflections). The compound crystallizes with a = 728.56(4), b = 989.51(6), c = 676.27(3) pm, β = 93.120(5)°, Z = 4 in space group P21/c of the pyrochlore related KCuCrF6 type. The octahedral coordinations [GaF6] and [CuF6] are slightly resp. strongly distorted (mean values Ga‐F: 188.2 pm resp. Cu‐F: 188.2/200.1/227.6 pm). The longest distances Ga‐F and the shortest ones Cu‐F are found within octahedral chains of these two kinds of atoms, running along [100] and [001], resp., and being mutually bridged as well (M‐F‐M in between 114 and 145°). The magnetic mole susceptibilities measured at powders and at a single crystal follow the isotropic Heisenberg model for S = 1/2, if effects of chain disrupture are considered in the form of some paramagnetic portion. No indication of threedimensional magnetic order is observed down to T = 2 K and low magnetic fields H < 100 G. KCuGaF6 (J/k = —71 K for the powder) is distinguished this way from the chain structure compounds KCuAlF6 und Na2CuScF7 (J/k = —76 resp. —59 K) which were also magnetically studied and yield similar antiferromagnetic exchange constants J/k. 相似文献
4.
5.
Stephan Dahlke Gitta Kutyniok Gabriele Steidl Gerd Teschke 《Applied and Computational Harmonic Analysis》2009,27(2):195-214
In this paper, we study the relationships of the newly developed continuous shearlet transform with the coorbit space theory. It turns out that all the conditions that are needed to apply the coorbit space theory can indeed be satisfied for the shearlet group. Consequently, we establish new families of smoothness spaces, the shearlet coorbit spaces. Moreover, our approach yields Banach frames for these spaces in a quite natural way. We also study the approximation power of best n-term approximation schemes and present some first numerical experiments. 相似文献
6.
7.
Stephan Dahlke Gabriele Steidl Gerd Teschke 《Journal of Fourier Analysis and Applications》2007,13(4):387-403
The topic of this article is a generalization of the theory of coorbit spaces and related frame constructions to Banach spaces
of functions or distributions over domains and manifolds. As a special case one obtains modulation spaces and Gabor frames
on spheres. Group theoretical considerations allow first to introduce generalized wavelet transforms. These are then used
to define coorbit spaces on homogeneous spaces, which consist of functions having their generalized wavelet transform in some
weighted Lp space. We also describe natural ways of discretizing those wavelet transforms, or equivalently to obtain atomic decompositions
and Banach frames for the corresponding coorbit spaces. Based on these facts we treat aspects of nonlinear approximation and
show how the new theory can be applied to the Gabor transform on spheres. For the S1 we exhibit concrete examples of admissible Gabor atoms which are very closely related to uncertainty minimizing states. 相似文献
8.
Elke Baum Patrik Dahlke Volker Kaiser Michel Molinier Roland E. Schmidt Jürgen Pebler Werner Massa Dietrich Babel 《无机化学与普通化学杂志》2006,632(14):2244-2250
9.
Stephan Dahlke 《manuscripta mathematica》1998,95(1):59-77
This paper is concerned with some theoretical foundations for adaptive numerical methods for elliptic boundary value problems.
The approximation order that can be achieved by such an adaptive method is determined by certain Besov regularity of the weak
solution. We study Besov regularity for second order elliptic problems in bounded domains in ℝ
d
. The investigations are based on intermediate Schauder estimates and on some potential theoretic framework. Moreover, we
use characterizations of Besov spaces by wavelet expansions.
This work has been supported by the Deutsche Forschungsgemeinschaft (Da 360/1-1) 相似文献
10.
Thomas Bonesky Stephan Dahlke Peter Maass Thorsten Raasch 《Advances in Computational Mathematics》2010,33(4):385-411
This paper is concerned with the numerical treatment of inverse heat conduction problems. In particular, we combine recent
results on the regularization of ill-posed problems by iterated soft shrinkage with adaptive wavelet algorithms for the forward
problem. The analysis is applied to an inverse parabolic problem that stems from the industrial process of melting iron ore
in a steel furnace. Some numerical experiments that confirm the applicability of our approach are presented. 相似文献