Micro-local analysis in Fourier Lebesgue and modulation spaces: part II
By Stevan Pilipovic, Nenad Teofanov, J. Toft. 2008
62 citations recorded by the source corpus.
AbstractWe consider different types of (local) products f1 f2 in Fourier Lebesgue spaces. Furthermore, we prove the existence of such products for other distributions satisfying appropriate wave-front properties. We also consider semi-linear equations of the form $$P(x,D)f = G(x,J_k f),$$with appropriate polynomials P and G, where Jk denotes the k-jet of f. If the solution locally belongs to appropriate weighted Fourier Lebesgue space $${\fancyscript{F}L^q_{(\omega )} (\mathbf{R}^d)}$$ and P is non-characteristic at (x0, ξ0), then we prove that $${(x_0,\xi_0)\not \in {\rm WF}_{\fancyscript{F}L^q_{(\widetilde {\omega })}} (f)}$$, where $${\widetilde{\omega }}$$ depends on ω, P and G.
Subfields: Applied Mathematics, Computer Vision and Pattern Recognition
View Paper: https://www.semanticscholar.org/paper/82215c5b0993b85177e03febb39c3835e42781fc
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In Applied Mathematics
- Nenad Teofanov
- Stevan Pilipovic
- J. Toft
- Karlheinz Gröchenig
- Mitsuru Sugimoto
- L. Rodino
- Hans G. Feichtinger
- Elena Cordero
In Computer Vision and Pattern Recognition
Citations in the corpus
- Micro-Local Analysis with Fourier Lebesgue Spaces. Part I (2011, methodology): “In the second paper [24]we consider products in Fourier Lebesgue spaces, related to the new notion of wave-fronts with applications to a class of semilinear partial differential equations.”