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Karoline Johansson

Publications and source records attributed to Karoline Johansson.

9 recordsLinked to original sources
arXiv2014

Global wave-front sets of Banach, Fr{é}chet and Modulation space types, and pseudo-differential operators

We introduce global wave-front sets $\operatorname{WF}_{\mathcal B} (f)$, $f\in {\mathscr S}^\prime(\textbf{R}^d)$, with respect to suitable Banach or Fréchet spaces ${\mathcal B}$. An important special case is given by the modulation spaces ${\mathcal B}=M(ω,\mathscr B)$, where $ω$ is an appropriate weight function and $\mathscr B$ is a translation invariant Banach function space. We show that the standard properties for known notions of wave-front set extend to $\operatorname{WF}_{\mathcal B} (f)$. In particular, we prove that micro locality and microellipticity hold for a class of globally defined pseudo-differential operators $\operatorname{Op}_t(a)$, acting continuously on the involved spaces.

math.FA↗
arXiv2011

Micro-local analysis in some spaces of ultradistributions

In this paper we extend some results from our earlier papers on wave-front sets, concerning wave-front sets of Fourier-Lebesgue and modulation space types, to a broader class of spaces of ultradistributions, and relate these wave-front sets with the usual wave-front sets of ultradistributions. Furthermore, we use Gabor frames for the description of discrete wave-front sets, and prove that these wave-front sets coincide with corresponding continuous ones.

math.FA↗
arXiv2011

Generalized free time-dependent Schrödinger equation with initial data in Fourier Lebesgue spaces

Consider the solution of the free time-dependent Schrödinger equation with initial data f. It is shown by Sjögren and Sjölin (1989) that there exists f in the Sobolev space H^s(R^d), s=d/2 such that tangential convergence can not be widened to convergence regions. In 2010 we obtained the corresponding results for a generalized version of the Schrödinger equation, where -Δ_x is replaced by an operator ϕ(D), with special conditions on ϕ. In this paper we show that similar results may be obtained for initial data in Fourier Lebesgue spaces.

math.AP↗
arXiv2010

Association between temperate distributions and analytical functions in the context of wave-front sets

Let B be a translation invariant Banach function space (BF-space). In this paper we prove that every temperate distribution f can be associated with a function F analytic in the convex tube Omega={z in C^d; |Im z|<1} such that the wave-front set of f of Fourier BF-space types in intersection with R^d \times S^{d-1} consists of the points (x,ξ) such that F does not belong to the Fourier BF-space at x-iξ.

math.FA↗
arXiv2009

Wave-front sets of Banach function types

We introduce the wave-front set for distributions with respect to Fourier images of weighted translation invariant Banach function spaces. We prove that usual mapping properties for pseudo-differential operators hold in the context of such wave-front sets.

math.FA↗
arXiv2008

A counter example on nontangential convergence for oscillatory integrals

Consider the solution of the time-dependent Schr{ö}dinger equation with initial data $f$. It is shown in \cite{artikel} that there exists $f$ in the Sobolev space $H^s(\RR), s=n/2$ such that tangential convergence can not be widened to convergence regions. In this paper we show that the corresponding result holds when $-Δ_x$ is replaced by an operator $ϕ(D)$, with special conditions on $ϕ$.

math.AP↗