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Johansson, Karoline
##### Publications (10 of 17) Show all publications
Coriasco, S., Johansson, K. & Toft, J. (2016). Global Wave-Front Properties for Fourier Integral Operators and Hyperbolic Problems. Journal of Fourier Analysis and Applications, 22(2), 285-333
Open this publication in new window or tab >>Global Wave-Front Properties for Fourier Integral Operators and Hyperbolic Problems
2016 (English)In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 22, no 2, p. 285-333Article in journal (Refereed) Published
##### Abstract [en]

We illustrate the composition properties for an extended family of SG Fourier integral operators. We prove continuity results on modulation spaces, and study mapping properties of global wave-front sets for such operators. These extend classical results to more general situations. For example, there are no requirements on homogeneity for the phase functions. Finally, we apply our results to the study of the propagation of singularities, in the context of modulation spaces, for the solutions to the Cauchy problems for the corresponding linear hyperbolic operators.

Springer, 2016
##### Keywords
Wave-front, Fourier integral operator, Banach, Modulation, Micro-local
##### National Category
Mathematical Analysis
##### Research subject
Mathematics, Mathematics
##### Identifiers
urn:nbn:se:lnu:diva-50410 (URN)10.1007/s00041-015-9422-1 (DOI)000376247200003 ()2-s2.0-84934780044 (Scopus ID)
##### Projects
Matematisk modellering Available from: 2016-03-09 Created: 2016-03-09 Last updated: 2017-11-30Bibliographically approved
Toft, J., Johansson, K., Pilipovic, S. & Teofanov, N. (2015). Sharp convolution and multiplication estimates in weighted spaces. Analysis and Applications, 13(5), 457-480
Open this publication in new window or tab >>Sharp convolution and multiplication estimates in weighted spaces
2015 (English)In: Analysis and Applications, ISSN 0219-5305, Vol. 13, no 5, p. 457-480Article in journal (Refereed) Published
##### Abstract [en]

We establish sharp convolution and multiplication estimates in weighted Lebesgue, Fourier Lebesgue and modulation spaces. We cover, especially some results in [L. Hörmander, Lectures on Nonlinear Hyperbolic Differential Equations (Springer, Berlin, 1997); S. Pilipović, N. Teofanov and J. Toft, Micro-local analysis in Fourier Lebesgue and modulation spaces, II, J. Pseudo-Differ. Oper. Appl.1 (2010) 341–376]. The results are also related to some results by Iwabuchi in [T. Iwabuchi, Navier–Stokes equations and nonlinear heat equations in modulation spaces with negative derivative indices, J. Differential Equations 248 (2010) 1972–2002].

##### Place, publisher, year, edition, pages
World Scientific, 2015
##### Keywords
Fourier; Lebesgue; modulation; sharpness, Inbäddningar, faltningar, modulationsrum, Fourier-Lebesguerum
##### National Category
Mathematical Analysis
##### Research subject
Natural Science, Mathematics
##### Identifiers
urn:nbn:se:lnu:diva-36180 (URN)10.1142/S0219530514500523 (DOI)000357134400001 ()2-s2.0-84934753270 (Scopus ID)
##### Projects
Matematisk modellering Available from: 2014-07-22 Created: 2014-07-22 Last updated: 2018-05-21Bibliographically approved
Coriasco, S., Johansson, K. & Toft, J. (2014). Global Wave-front Sets of Intersection and Union Type. In: Michael Ruzhansky, Ville Turunen (Ed.), Fourier Analysis: Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations (pp. 91-106). Heidelberg, New York, Dordrecht, London: Springer
Open this publication in new window or tab >>Global Wave-front Sets of Intersection and Union Type
2014 (English)In: Fourier Analysis: Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations / [ed] Michael Ruzhansky, Ville Turunen, Heidelberg, New York, Dordrecht, London: Springer, 2014, p. 91-106Chapter in book (Refereed)
##### Abstract [en]

We show that a temperate distribution belongs to an ordered intersection or union of admissible Banach or Fréchet spaces if and only if the corresponding global wave-front set of union or intersection type is empty. We also discuss the situation where intersections and unions of sequences of spaces with two indices are involved. A main situation where the present theory applies is given by sequences of weighted, general modulation spaces.

##### Place, publisher, year, edition, pages
Heidelberg, New York, Dordrecht, London: Springer, 2014
##### Series
Trends in Mathematics
##### Keywords
Wave-front, Fourier, Banach space, modulation space, micro-local, pseudo-differential
##### National Category
Mathematical Analysis
##### Research subject
Mathematics, Mathematics
##### Identifiers
urn:nbn:se:lnu:diva-52520 (URN)10.1007/978-3-319-02550-6_5 (DOI)2-s2.0-84959093759 (Scopus ID)978-3-319-02549-0 (ISBN)978-3-319-02550-6 (ISBN)
##### Note

Ingår i matematisk modellering och ICMM

Available from: 2016-05-17 Created: 2016-05-17 Last updated: 2017-01-11Bibliographically approved
Johansson, K., Pilipovic, S., Teofanov, N. & Toft, J. (2013). A note on wave-front sets of Roumieu type ultradistributions. In: S. Molahajlo, S. Pilipovic, J. Toft, M. W. Wong (Ed.), Pseudo-Differential Operators, Generalized Functionsand Asymptotics: (pp. 239-252). Basel Heidelberg NewYork Dordrecht London: Springer
Open this publication in new window or tab >>A note on wave-front sets of Roumieu type ultradistributions
2013 (English)In: Pseudo-Differential Operators, Generalized Functionsand Asymptotics / [ed] S. Molahajlo, S. Pilipovic, J. Toft, M. W. Wong, Basel Heidelberg NewYork Dordrecht London: Springer, 2013, p. 239-252Chapter in book (Refereed)
##### Abstract [en]

We study wave-front sets in weighted Fourier–Lebesgue spaces and corresponding spaces of ultradistributions. We give a comparison of these sets with the well-known wave-front sets of Roumieu type ultradistributions. Then we study convolution relations in the framework of ultradistributions. Finally, we introduce modulation spaces and corresponding wave-front sets, and establish invariance properties of such wave-front sets.

##### Place, publisher, year, edition, pages
Basel Heidelberg NewYork Dordrecht London: Springer, 2013
##### Series
Operator Theory: Advances and applications ; 231
##### National Category
Mathematical Analysis
##### Research subject
Mathematics, Mathematics
##### Identifiers
urn:nbn:se:lnu:diva-52519 (URN)10.1007/978-3-0348-0585-8_12 (DOI)
##### Projects
Matematisk modellering, ICMM Available from: 2016-05-17 Created: 2016-05-17 Last updated: 2017-03-09Bibliographically approved
Coriasco, S., Johansson, K. & Toft, J. (2013). Global wave-front sets of Banach, Fréchet and Modulation spacetypes, and pseudo-differential operators. Journal of Differential Equations, 254(8), 3228-3258
Open this publication in new window or tab >>Global wave-front sets of Banach, Fréchet and Modulation spacetypes, and pseudo-differential operators
2013 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 254, no 8, p. 3228-3258Article in journal (Refereed) Published
##### Abstract [en]

We introduce global wave-front sets with respect to suitable Banach or Fréchet spaces. An important special case appears when choosing these spaces as modulation spaces. We show that the standard properties for known notions of wave-front set extend to global wave-front sets. In particular, we prove that microlocality and microellipticity hold for a class of globally defined pseudo-differential operators, acting continuously on the involved spaces.

##### National Category
Mathematical Analysis
##### Research subject
Mathematics, Mathematics
##### Identifiers
urn:nbn:se:lnu:diva-23455 (URN)10.1016/j.jde.2013.01.014 (DOI)000315831000004 ()2-s2.0-84874225584 (Scopus ID)
##### Projects
Matematisk modellering Available from: 2013-01-14 Created: 2013-01-14 Last updated: 2017-12-06Bibliographically approved
Coriasco, S., Johansson, K. & Toft, J. (2013). Local wave-front sets of Banach and Fréchet types, and pseudo-differential operators. Monatshefte für Mathematik (Print), 169(3-4), 285-316
Open this publication in new window or tab >>Local wave-front sets of Banach and Fréchet types, and pseudo-differential operators
2013 (English)In: Monatshefte für Mathematik (Print), ISSN 0026-9255, E-ISSN 1436-5081, Vol. 169, no 3-4, p. 285-316Article in journal (Refereed) Published
##### Abstract [en]

Let ω, ω 0 be appropriate weight functions and ${\fancyscript{B}}$ be an invariant BF-space. We introduce the wave-front set ${{\rm WF}_{\mathcal{B}}(f)}$ with respect to the weighted Fourier Banach space ${\mathcal{B}=\fancyscript{F} \fancyscript{B}(\omega )}$ . We prove that the usual mapping properties for pseudo-differential operators Op t (a) with symbols a in ${S^{(\omega_0)}_{\rho, 0}}$ hold for such wave-front sets. In particular we prove ${{\rm WF}_{\mathcal C}({\rm Op}_t (a) f)\subseteq {\rm WF}_{\mathcal{B}}(f)}$ and ${{\rm WF}_{\mathcal{B}}(f) \subseteq {\rm WF} _{\mathcal C}({\rm Op}_t (a) f)\bigcup {\rm Char} (a)}$ . Here ${\mathcal{C}=\fancyscript{F} \fancyscript{B}(\omega /\omega_0)}$ and Char(a) is the set of characteristic points of a.

Springer, 2013
##### Keywords
Wave-front, Fourier, Banach, Modulation, Micro-local
##### National Category
Mathematical Analysis
##### Research subject
Natural Science, Mathematics
##### Identifiers
urn:nbn:se:lnu:diva-16966 (URN)10.1007/s00605-012-0392-y (DOI)000314843500003 ()2-s2.0-84874021235 (Scopus ID)
##### Projects
Matematisk modellering Available from: 2012-01-21 Created: 2012-01-21 Last updated: 2017-12-08Bibliographically approved
Johansson, K., Pilipovic, S., Teofanov, N. & Toft, J. (2013). Resolution of the wave- front set via discrete sets. Proceedings in Applied Mathematics and Mechanics: PAMM, 13, 495-496
Open this publication in new window or tab >>Resolution of the wave- front set via discrete sets
2013 (English)In: Proceedings in Applied Mathematics and Mechanics: PAMM, ISSN 1617-7061, E-ISSN 1617-7061, Vol. 13, p. 495-496Article in journal (Refereed) Published
##### Abstract [en]

We introduce discrete wave-front sets of sup type and prove that they coincide with the Hörmander wave-front set of a distribution. To that end we recall the notion of admissible lattice pairs and wave-front sets in Fourier-Lebesgue spaces.

Wiley, 2013
##### National Category
Mathematical Analysis
##### Research subject
Mathematics, Mathematics
##### Identifiers
urn:nbn:se:lnu:diva-52524 (URN)10.1002/pamm.201310240 (DOI)
##### Projects
Matematisk modellering ICMM Available from: 2016-05-17 Created: 2016-05-17 Last updated: 2017-11-30Bibliographically approved
Johansson, K., Pilipovic, S., Teofanov, N. & Toft, J. (2012). Gabor pairs, and a discrete approach to wave-front sets. Monatshefte für Mathematik (Print), 166(2), 181-199
Open this publication in new window or tab >>Gabor pairs, and a discrete approach to wave-front sets
2012 (English)In: Monatshefte für Mathematik (Print), ISSN 0026-9255, E-ISSN 1436-5081, Vol. 166, no 2, p. 181-199Article in journal (Refereed) Published
##### Abstract [en]

We introduce admissible lattices and Gabor pairs to define discrete versions of wave-front sets with respect to Fourier Lebesgue and modulation spaces. We prove that these wave-front sets agree with each other and with corresponding wave-front sets of "continuous type". This implies that the coefficients of a Gabor frame expansion of $f$ are parameter dependent, and describe the wave-front set of $f$.

Springer, 2012
##### National Category
Mathematical Analysis
##### Research subject
Natural Science, Mathematics
##### Identifiers
urn:nbn:se:lnu:diva-10207 (URN)10.1007/s00605-011-0288-2 (DOI)2-s2.0-84860218805 (Scopus ID)
##### Projects
matematisk modellering Available from: 2011-01-19 Created: 2011-01-19 Last updated: 2017-12-11Bibliographically approved
Johansson, K., Pilipovic, S., Teofanov, N. & Toft, J. (2012). Micro-local analysis in some spaces of ultradistributions. Publications de l'Institut Mathématique (Beograd), 92(106), 1-24
Open this publication in new window or tab >>Micro-local analysis in some spaces of ultradistributions
2012 (English)In: Publications de l'Institut Mathématique (Beograd), ISSN 0350-1302, E-ISSN 1820-7405, Vol. 92, no 106, p. 1-24Article in journal (Refereed) Published
##### Abstract [en]

We extend some results from [14] and [19], concerning wave-front sets of Fourier–Lebesgue and modulation space types, to a broader class of spaces of ultradistributions. We relate these wave-front sets one to another and to the usual wave-front sets of ultradistributions.

Furthermore, we give a description of discrete wave-front sets by intro- ducing the notion of discretely regular points, and prove that these wave-front sets coincide with corresponding wave-front sets in [19]. Some of these inves- tigations are based on the properties of the Gabor frames.

##### Keywords
Wave-front sets, weighted Fourier-Lebesgue spaces, ultradistributions
##### National Category
Mathematical Analysis
##### Research subject
Mathematics, Mathematics
##### Identifiers
urn:nbn:se:lnu:diva-22564 (URN)10.2298/PIM1206001J (DOI)2-s2.0-84873032464 (Scopus ID)
##### Projects
Matematisk modellering Available from: 2012-11-21 Created: 2012-11-21 Last updated: 2017-12-07Bibliographically approved
Johansson, K. (2011). Association between temperate distributions and analytical functions in the context of wave-front sets. Journal of Pseudo-Differential Operators and Applications, 2(1), 65-89
Open this publication in new window or tab >>Association between temperate distributions and analytical functions in the context of wave-front sets
2011 (English)In: Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, E-ISSN 1662-999X, Vol. 2, no 1, p. 65-89Article in journal (Refereed) Published
##### Abstract [en]

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 Ω = {z in Cd; | Im z| < 1 } such that the wave-front set of f of Fourier BF-space types in intersection with Rd ×Sd-1 consists of the points (x, ξ) such that F does not belong to the Fourier BF-space at xi ξ.

##### Place, publisher, year, edition, pages
Basel: Birkhäuser, 2011
##### Keywords
Analytic function, Wave-front set, Fourier Banach function space
##### National Category
Mathematical Analysis
##### Research subject
Mathematics, Mathematics
##### Identifiers
urn:nbn:se:lnu:diva-11101 (URN)10.1007/s11868-011-0022-9 (DOI)2-s2.0-84873023894 (Scopus ID)
Available from: 2011-03-15 Created: 2011-03-12 Last updated: 2017-12-11Bibliographically approved

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