arXiv subjects

Nenad Teofanov

Publications and source records attributed to Nenad Teofanov.

39 records · Page 3Linked to original sources

arXiv2009

Micro-local analysis in Fourier Lebesgue and modulation spaces. Part I

Let $ω,ω_0$ be appropriate weight functions and $q\in [1,\infty ]$. We introduce the wave-front set, $\WF_{\mathscr FL^q_{(ω)}}(f)$ of $f\in \mathscr S'$ with respect to weighted Fourier Lebesgue space $\mathscr FL^q_{(ω)}$. We prove that usual mapping properties for pseudo-differential operators $\op (a)$ with symbols $a$ in $S^{(ω_0)}_{ρ, 0}$ hold for such wave-front sets. Especially we prove \WF_{\mathscr FL^q_{(ω/ω_0)}}(\op (a)f)\subseteq \WF_{\mathscr FL^q_{(ω)}}(f) \subseteq \WF_{\mathscr FL^q_{(ω/ω_0)}}(\op (a)f)\ttbigcup \Char (a). %% Here $\Char (a)$ is the set of characteristic points of $a$.

math.AP↗

arXiv2009

Discrete Wave-front sets of Fourier Lebesgue and modulation space types

We introduce discrete wave-front sets with respect to Fourier Lebesgue and modulation spaces. We prove that these wave-front sets agree with corresponding wave-front sets of "continuous type".

math.FA↗

arXiv2009

Micro-local analysis in Fourier Lebesgue and modulation spaces. Part II

We consider different types of (local) products $f_1 f_2$ 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 $$ \qquad P(x,D)f = G(x,J_k f), $$ with appropriate polynomials $P $ and $G$. If the solution locally belongs to appropriate weighted Fourier Lebesgue space ${\mathscr F}L^q_{(ω)} (\rr d)$ and $P$ is non-characteristic at $(x_0,ξ_0),$ then we prove that $(x_0,ξ_0)\not \in WF_{{\mathscr F}L^q_{(\widetilde ω)}} (f)$, where $\widetildeω$ depends on $ω$, $P$ and $G$.

math.FA↗