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It is shown that the Hankel transformation Hsub(v) acts in a class of weighted Sobolev spaces. Especially, the isometric mapping property of Hsub(v) which holds on L²(IRsub(+),rdr) is extended to spaces of arbitrary Sobolev order. The novelty in the approach consists in using techniques developed by B.-W. Schulze and others to treat the half-line Rsub(+) as a manifold with a conical singularity at r = 0. This is achieved by pointing out a connection between the Hankel transformation and the Mellin transformation.The procedure proposed leads at the same time to a short proof of the Hankel inversion formula. An application to the existence and higher regularity of solutions, including their asymptotics, to the 1-1-dimensional edge-degenerated wave equation is given.
Die Untersuchungen machen wahrscheinlich, daß ein Reichsministerialengeschlecht vor 1161 den Raum Treuenbrietzen okkupierte, dort einen Herrschaftssitz errichtete und mit einem ersten Landesausbau begann. Zwischen 1194 und 1208 endete die relative Selbständigkeit dieses Geschlechts. Brietzen wurde Bestandteil der erzbischöflich-magdeburgischen Territorialherrschaft Jüterbog, ging aber noch im 13. Jahrhundert in brandenburgisch-askanischen Besitz über.
Vor- und nacheiszeitliche Großtierformen in Mitteleuropa und ihre Einpassung in das Ökosystem
(1997)
We have studied the bifurcation structure of the incompressible two-dimensional Navier-Stokes equations with a special external forcing driving an array of 8×8 counterrotating vortices. The study has been motivated by recent experiments with thin layers of electrolytes showing, among other things, the formation of large-scale spatial patterns. As the strength of the forcing or the Reynolds number is raised the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. The bifurcations lead to several periodic branches, torus and chaotic solutions, and other stationary solutions. Most remarkable is the appearance of solutions characterized by structures on spatial scales large compared to the scale of the forcing. We also characterize the different dynamic regimes by means of tracers injected into the fluid. Stretching rates and Hausdorff dimensions of convected line elements are calculated to quantify the mixing process. It turns out that for time-periodic velocity fields the mixing can be very effective.
In the rapidly growing literature on globalization, many authors have emphasized the apparent disembedding of social relations from their local-territorial preconditions. Such arguments neglect the relatively fixed and immobile forms of territorial organization upon which the current round of globalization is premised, such as urban-regional agglomerations and territorial states. Drawing on the work of David Harvey and Henri Lefebvre, this article argues that processes of reterritorialization - the reconfiguration of forms of terrritorial organization such as cities and states - must be viewed as an intrinsic moment of the current round of globalization. Globalization is conceived here as a reterritorialization of both socio-economic and political-institutional spaces that unfolds simultaneously upon multiple, superimposed geographical scales. The ongoing restructuring of contemporary urban spaces and state institutional-territorial structures must be viewed at once as presupposition, a medium and an outcome of this highly contested dynamic of global spatial restructuring. New theories and representations of the scaling of spatial practices are needed to grasp the rapidly changing territorial organization of world capitalism in the late 20th century.