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Summary In this paper, we develop a framework suitable for performing a multiresolution analysis using univariate spline spaces of arbitrary degree and with non-uniform knot-sequences. To this end, we show, among other things, the existence of compactly supported prewavelets and of prewavelets that are globally supported, but decay exponentially. In each case we obtain a decomposition of a fine spline space as a sum of a coarse spline space plus a spline space spanned by prewavelets. 相似文献
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M. D. Buhmann 《Constructive Approximation》1990,6(3):225-255
For a radial-basis function?∶?→? we consider interpolation on an infinite regular lattice , tof∶? n→?, whereh is the spacing between lattice points and the cardinal function , satisfiesX(j)=δ oj for allj∈? n. We prove existence and uniqueness of such cardinal functionsX, and we establish polynomial precision properties ofI h for a class of radial-basis functions which includes \(\varphi (r) = r^{2q + 1} \) , \(\varphi (r) = r^{2q} \log r,\varphi (r) = \sqrt {r^2 + c^2 } \) , and \(\varphi (r) = 1/\sqrt {r^2 + c^2 } \) whereq∈? +. We also deduce convergence orders ofI hf to sufficiently differentiable functionsf whenh→0. 相似文献
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Wang J Beton PH Mori N Eaves L Buhmann H Mansouri L Main PC Foster TJ Henini M 《Physical review letters》1994,73(8):1146-1149
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The van der Waals potential of two atoms in the presence of an arbitrary arrangement of dispersing and absorbing magnetoelectric
bodies is studied. Starting from a polarizable atom placed within a given geometry, its interaction with a second polarizable/magnetizable
atom is deduced from its Casimir-Polder interaction with a weakly polarizable/magnetizable test body. The general expressions
for the van der Waals potential obtained thusly are illustrated by considering first the case of two atoms in free space,
with special emphasis on the interaction between (i) two polarizable atoms and (ii) a polarizable and a magnetizable atom.
Furthermore, the influence of magnetoelectric bodies on the van der Waals interaction is studied in detail for the example
of two atoms placed near a perfectly reflecting plate or a magnetoelectric half space, respectively.
The text was submitted by the authors in English. 相似文献
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König M Tschetschetkin A Hankiewicz EM Sinova J Hock V Daumer V Schäfer M Becker CR Buhmann H Molenkamp LW 《Physical review letters》2006,96(7):076804
Ring structures fabricated from HgTe/HgCdTe quantum wells have been used to study Aharonov-Bohm type conductance oscillations as a function of Rashba spin-orbit splitting strength. We observe nonmonotonic phase changes indicating that an additional phase factor modifies the electron wave function. We associate these observations with the Aharonov-Casher effect. This is confirmed by comparison with numerical calculations of the magnetoconductance for a multichannel ring structure within the Landauer-Büttiker formalism. 相似文献
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