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Diffraction from conormal singularities
Diffraction conormal singularities Analysis of PDEs
2012/4/23
In this paper we show that for metrics with conormal singularities that correspond to class C^{1,\alpha} with \alpha>0, the reflected wave is more regular than the incident wave in a Sobolev sense. Th...
Random fields on model sets with localized dependency and their diffraction
Diffraction Pure point spectrum Absolutely continuous spectrum Quasicrystal Model set
2011/9/19
Abstract: For a random field on a general discrete set, we introduce a condition that the range of the correlation from each site is within a predefined compact set D. For such a random field {\omega}...
Close-packed dimers on the line: diffraction versus dynamical spectrum
Close-packed dimers line diffraction versus dynamical spectrum
2010/11/12
The translation action of $\RR^{d}$ on a translation bounded measure $\omega$ leads to an interesting class of dynamical systems, with a rather rich spectral theory. In general, the diffraction spect...
Strongly Elliptic Operators for a Plane Wave Diffraction Problem in Bessel Potential Spaces
Diffraction problem Strong Ellipticity Convolution type operator Wiener-Hopf operator Equivalence after extension
2008/6/26
We consider a plane wave diffraction problem by a union of several infinite strips. The problem is formulated as a boundary-transmission one for the Helmholtz equation in a Bessel potential space sett...