In this work, we establish certain equivalences between the localisation properties with respect ... more In this work, we establish certain equivalences between the localisation properties with respect to spherical Fourier means of the support of a given Borel measure and the L 2-rate of decay of the Fourier extension operator associated to it. This, in turn, is intimately connected with the property that the X-ray transform of the measure be uniformly bounded. Geometric properties of sets supporting such a measure are studied.
In this work, we establish certain equivalences between the localisation properties with respect ... more In this work, we establish certain equivalences between the localisation properties with respect to spherical Fourier means of the support of a given Borel measure and the L 2-rate of decay of the Fourier extension operator associated to it. This, in turn, is intimately connected with the property that the X-ray transform of the measure be uniformly bounded. Geometric properties of sets supporting such a measure are studied.
In this work, we establish certain equivalences between the localisation properties with respect ... more In this work, we establish certain equivalences between the localisation properties with respect to spherical Fourier means of the support of a given Borel measure and the L 2-rate of decay of the Fourier extension operator associated to it. This, in turn, is intimately connected with the property that the X-ray transform of the measure be uniformly bounded. Geometric properties of sets supporting such a measure are studied.
In this work, we establish certain equivalences between the localisation properties with respect ... more In this work, we establish certain equivalences between the localisation properties with respect to spherical Fourier means of the support of a given Borel measure and the L 2-rate of decay of the Fourier extension operator associated to it. This, in turn, is intimately connected with the property that the X-ray transform of the measure be uniformly bounded. Geometric properties of sets supporting such a measure are studied.
In this work, we establish certain equivalences between the localisation properties with respect ... more In this work, we establish certain equivalences between the localisation properties with respect to spherical Fourier means of the support of a given Borel measure and the L 2-rate of decay of the Fourier extension operator associated to it. This, in turn, is intimately connected with the property that the X-ray transform of the measure be uniformly bounded. Geometric properties of sets supporting such a measure are studied.
In this work, we establish certain equivalences between the localisation properties with respect ... more In this work, we establish certain equivalences between the localisation properties with respect to spherical Fourier means of the support of a given Borel measure and the L 2-rate of decay of the Fourier extension operator associated to it. This, in turn, is intimately connected with the property that the X-ray transform of the measure be uniformly bounded. Geometric properties of sets supporting such a measure are studied.
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