Joachim Toft

I have been employed at Linnaeus/Växjö university since 2004. My activity mainly concerns teaching and research. Before I came to Växjö, I was employed as assistant professor at Blekinge Institute of Technology in Karlskrona, Blekinge, Sweden. I became finished with my Ph.D. in mathematics at Lund University, Sweden during 1997. During 1995-1998 I was employed as teaching assistant master at Kristianstad University.

I am overwhelming enthusiastic to work at a university where "Become a Change Maker" is fundamental, a phrase based on academic brilliance and knowledge excellence. Unfortunately, I myself do not reach this level, as I only succeeded at best to "Become a Fake Maker", but otherwise have to settle for "Become a Pain Maker". Hopefully I will improve in the future.

Teaching

During my academical career I have taught courses like basic mathematics, real analysis, multi-variable analysis, basic algebra, linear algebra, vector analysis, complex analysis, abstract algebra, statistics, measure and integration theory, functional analysis, distribution theory, as well as some Ph.D. courses in mathematics.

Research

My research mainly concerns pseudo-differential calculus and related topics, e.g. Fourier analysis, time-frequency analysis, harmonic analysis, basic operator theory, generalized functions (especially Gelfand-Shilov spaces and Gevrey classes) and micro-local analysis. Some research steps towards complex analysis have also been performed.

In my approach, functional analysis, harmonic analysis and basic operator theory are more frequently used comparing to what is usual within these fields. I am also interested in applications, especially concerning different types of wave phenomena, e.g. interpretations in physics, non-stationary filters, geophysics.

Commissions

Member of the mathematic organization ISAAC (International Society of Analysis it's Applications and Computations).

Editor of the following journals:

Journal of Pseudo-Differential Operators and Applications

Annals of Functional Analysis

My research groups

My ongoing research projects

Project: Hörmander-Weyl calculus in the framework of ultra distributions This project concerns developing a calculus of Weyl operators, also feasible for objects which are more hard treated than…

Publications

Article in journal (Refereed)

Gumber, A., Rana, N., Toft, J., Üster, R. (2024). Pseudo-differential calculi and entropy estimates with Orlicz modulation spaces. Journal of Functional Analysis. 286 (3).
Status: Published
Gröchenig, K., Pfeuffer, C., Toft, J. (2024). Spectral invariance of quasi-Banach algebras of matrices and pseudodifferential operators. Forum mathematicum.
Status: Epub ahead of print
Toft, J., Gumber, A. (2023). Fourier characterizations of Pilipović spaces. Journal of Functional Analysis. 284 (1).
Status: Published
Toft, J., Uster, R. (2023). Pseudo-differential operators on Orlicz modulation spaces. Journal of Pseudo-Differential Operators and Applications. 14 (1).
Status: Published
Toft, J., Bhimani, D.G., Manna, R. (2023). Trace mappings on quasi-Banach modulation spaces and applications to pseudo-differential operators of amplitude type. Analysis and Applications. 21 (2). 453-495.
Status: Published
Toft, J., Bhimani, D.G., Manna, R. (2023). Fractional Fourier transforms, harmonic oscillator propagators and Strichartz estimates on Pilipovic and modulation spaces. Applied and Computational Harmonic Analysis. 67.
Status: Published
Toft, J. (2022). Wick and Anti-Wick Characterizations of Linear Operators on Spaces of Power Series Expansions. Journal of Fourier Analysis and Applications. 28 (5).
Status: Published
Toft, J. (2022). Step multipliers, Fourier step multipliers and multiplications on quasi-Banach modulation spaces. Journal of Functional Analysis. 282 (5).
Status: Published
Teofanov, N., Toft, J., Wahlberg, P. (2022). Pseudo-differential operators with isotropic symbols, Wick and anti-Wick operators, and hypoellipticity. Journal des Mathématiques Pures et Appliquées. 167. 48-100.
Status: Published
Toft, J., Üster, R., Nabizadeh Morsalfard, E., Öztop, S. (2022). Continuity properties and Bargmann mappings of quasi-Banach Orlicz modulation spaces. Forum mathematicum. 34 (5). 1205-1232.
Status: Published
Toft, J. (2021). The Zak Transform on Gelfand-Shilov and Modulation Spaces with Applications to Operator Theory. Complex Analysis and Operator Theory. 15 (1). 1-42.
Status: Published
Toft, J., Gumber, A., Manna, R., Ratnakumar, P.K. (2021). Translation and modulation invariant Hilbert spaces. Monatshefte für Mathematik (Print). 196. 389-398.
Status: Published
Teofanov, N., Toft, J. (2020). Pseudo-differential calculus in a Bargmann setting. Annales Academiae Scientiarum Fennicae Mathematica. 45. 227-257.
Status: Published
Abdeljawad, A., Fernandez, C., Galbis, A., Toft, J., Uster, R. (2020). Characterizations of a class of Pilipovic spaces by powers of harmonic oscillator. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 114 (3). 1-13.
Status: Published
Toft, J. (2020). Paley-Wiener properties for spaces of power series expansions. Complex Variables and Elliptic Equations. 65 (10). 1698-1716.
Status: Published
Toft, J. (2020). Tensor products for Gelfand–Shilov and Pilipović distribution spaces. Journal of Analysis. 28. 591-613.
Status: Published
Abdeljawad, A., Coriasco, S., Toft, J. (2020). Liftings for ultra-modulation spaces, and one-parameter groups of Gevrey-type pseudo-differential operators. Analysis and Applications. 18 (4). 523-583.
Status: Published
Nabizadeh Morsalfard, E., Pfeuffer, C., Toft, J. (2020). Paley-Wiener properties for spaces of entire functions. Analysis and Mathematical Physics. 10 (2). 1-34.
Status: Published
De Gosson, M., Toft, J. (2020). Continuity Properties for Born-Jordan Operators with Symbols in Hörmander Classes and Modulation Spaces. Acta Mathematica Scientia. 40 (6). 1603-1626.
Status: Published
Toft, J. (2019). Continuity of Gevrey-Hörmander pseudo-differential operators on modulation spaces. Journal of Pseudo-Differential Operators and Applications. 10 (2). 337-358.
Status: Published
Chen, Y., Toft, J., Wahlberg, P. (2019). The Weyl product on quasi-Banach modulation spaces. Bulletin of Mathematical Sciences. 9 (2). 1-30.
Status: Published
Abdeljawad, A., Cappiello, M., Toft, J. (2019). Pseudo-Differential Calculus in Anisotropic Gelfand-Shilov Setting. Integral equations and operator theory. 91 (3).
Status: Published
Toft, J. (2019). Schatten properties, nuclearity and minimality of phase shift invariant spaces. Applied and Computational Harmonic Analysis. 46 (1). 154-176.
Status: Published
Ivanenko, Y., Gustafsson, M., Jonsson, B.L.G., Luger, A., Nilsson, B., et al. (2019). Passive Approximation and Optimization Using B-Splines. SIAM Journal on Applied Mathematics. 79 (1). 436-458.
Status: Published
Pilipovic, S., Toft, J. (2019). Wave-front sets related to quasi-analytic Gevrey sequences. Publications de l'Institut Mathématique (Beograd). 105 (119). 1-16.
Status: Published
Pfeuffer, C., Toft, J. (2019). Compactness Properties for Modulation Spaces. Complex Analysis and Operator Theory. 13 (8). 3521-3548.
Status: Published
Chen, Y., Signahl, M., Toft, J. (2018). Factorizations and singular value estimates of operators with Gelfand-Shilov and Pilipovic' kernels. Journal of Fourier Analysis and Applications. 24 (3). 666-698.
Status: Published
Toft, J., Nabizadeh Morsalfard, E. (2018). Periodic distributions and periodic elements in modulation spaces. Advances in Mathematics. 323. 193-225.
Status: Published
Fernandez, C., Galbis Verdu, A., Toft, J. (2017). The Bargmann transform and powers of harmonic oscillator on Gelfand-Shilov subspaces. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 111 (1). 1-13.
Status: Published
Toft, J. (2017). Images of function and distribution spaces under the Bargmann transform. Journal of Pseudo-Differential Operators and Applications. 8 (1). 83-139.
Status: Published
Cappiello, M., Toft, J. (2017). Pseudo-differential operators in a Gelfand–Shilov setting. Mathematische Nachrichten. 290 (5-6). 738-755.
Status: Published
Toft, J. (2017). Continuity and compactness for pseudo-differential operators with symbols in quasi-Banach spaces or Hörmander classes. Analysis and Applications. 15 (3). 353-389.
Status: Published
Coriasco, S., Toft, J. (2016). A calculus of Fourier integral operators with inhomogeneous phase functions on R^d. Indian journal of pure and applied mathematics. 47 (1). 125-166.
Status: Published
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.
Status: Published
Chen, Y., Toft, J. (2015). Boundedness of Gevrey and Gelfand-Shilov kernels of positive semi-definite operators. Journal of Pseudo-Differential Operators and Applications. 6 (2). 153-185.
Status: Published
Cappiello, M., Rodino, L., Toft, J. (2015). On the Inverse to the Harmonic Oscillator. Communications in Partial Differential Equations. 40 (6). 1096-1118.
Status: Published
Toft, J., Johansson, K., Pilipovic, S., Teofanov, N. (2015). Sharp convolution and multiplication estimates in weighted spaces. Analysis and Applications. 13 (5). 457-480.
Status: Published
Fernandez, C., Galbis, A., Toft, J. (2015). Characterizations of GRS-weights, and consequences in time-frequency analysis. Journal of Pseudo-Differential Operators and Applications. 6 (3). 383-390.
Status: Published
Coriasco, S., Toft, J. (2014). Asymptotic expansions for Hörmander symbol classes in the calculus of pseudo-differential operators. Journal of Pseudo-Differential Operators and Applications. 5 (1). 27-41.
Status: Published
Cappiello, M., Rodino, L., Toft, J. (2014). Radial symmetric elements and the Bargmann transform. Integral transforms and special functions. 25 (9). 756-764.
Status: Published
Cordero, E., Toft, J., Wahlberg, P. (2014). Sharp results for the Weyl product on modulation spaces. Journal of Functional Analysis. 267 (8). 3016-3057.
Status: Published
Fernandez, C., Galbis, A., Toft, J. (2014). Spectral properties for matrix algebras. Journal of Fourier Analysis and Applications. 20 (2). 362-383.
Status: Published
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.
Status: Published
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.
Status: Published
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.
Status: Published
Gröchenig, K., Toft, J. (2013). The Range of Localization Operators and Lifting Theorems for Modulation and Bargmann-Fock Spaces. Transactions of the American Mathematical Society. 365 (8). 4475-4496.
Status: Published
Signahl, M., Toft, J. (2012). Mapping properties for the Bargmann transform on modulation spaces. Journal of Pseudo-Differential Operators and Applications. 3 (1). 1-30.
Status: Published
Nordebo, S., Gustafsson, M., Khrennikov, A., Nilsson, B., Toft, J. (2012). Fisher information for inverse problems and trace class operators. Journal of Mathematical Physics. 53 (12).
Status: Published
Toft, J. (2012). The Bargmann transform on modulation and Gelfand-Shilov spaces, with applications to Toeplitz and pseudo-differential operators. Journal of Pseudo-Differential Operators and Applications. 3 (2). 145-227.
Status: Published
Toft, J., Khrennikov, A., Nilsson, B., Nordebo, S. (2012). Decompositions of Gelfand-Shilov kernels into kernels of similar class. Journal of Mathematical Analysis and Applications. 396 (1). 315-322.
Status: Published
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.
Status: Published
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.
Status: Published
Toft, J., Wahlberg, P. (2012). Embeddings of alpha-modulation spaces. Pliska Studia Mathematica Bulgarica. 21. 25-46.
Status: Published
Gröchenig, K., Toft, J. (2011). Isomorphism properties of Toeplitz operators and pseudo-differential operators between modulation spaces. Journal d'Analyse Mathematique. 114 (1). 255-283.
Status: Published
Ruzhansky, M., Sugimoto, M., Toft, J., Tomita, N. (2011). Changes of variables in modulation and Wiener amalgam spaces. Mathematische Nachrichten. 284 (16). 2078-2092.
Status: Published
Pilipovic, S., Teofanov, N., Toft, J. (2011). Micro-Local Analysis in Fourier Lebesgue and modulation Spaces. Part I. Journal of Fourier Analysis and Applications. 17 (3). 374-407.
Status: Published
Signahl, M., Toft, J. (2011). Remarks on mapping properties for the Bargmann transform on modulation spaces. Integral transforms and special functions. 22 (4-5). 359-366.
Status: Published
Toft, J., Pilipovic, S., Teofanov, N. (2010). Micro-local analysis in Fourier Lebesgue and modulation spaces. Part II. Journal of Pseudo-Differential Operators and Applications. 1 (3). 341-376.
Status: Published
Toft, J. (2010). Multiplication properties in pseudo-differential calculus with small regularity on the symbols. Journal of Pseudo-Differential Operators and Applications. 1 (1). 101-138.
Status: Published
Toft, J., Buzano, E. (2010). Schatten-von Neumann properties in the Weyl calculus. Journal of Functional Analysis. 259. 3080-3114.
Status: Published
Toft, J., Concetti, F., Garello, G. (2010). Schatten-von Neumann properties for Fourier integral operators with non-smooth symbols, II. Osaka Journal of Mathematics. 47 (2). 739-786.
Status: Published
Toft, J., Concetti, F. (2009). Schatten-von Neumann properties for Fourier integral operators with non-smooth symbols, I. Arkiv för matematik. 47. 295-312.
Status: Published
Toft, J. (2009). Pseudo-differential operators with smooth symbols on modulation spaces. CUBO. 11 (4). 87-107.
Status: Published
Pilipovic, S., Teofanov, N., Toft, J. (2008). Wave-front sets in Fourier Lebesgue Spaces. Rendiconti del seminario matematico. 66 (4). 299-320.
Status: Published
Toft, J., Paolo, B. (2008). Schatten classes for Toeplitz operators with Hilbert space windows on modulation spaces. Advances in Mathematics. 217 (1). 305-333.
Status: Published
Toft, J., Holst, A., Wahlberg, P. (2007). Weyl product algebras and modulation spaces. Journal of functional analysis. 251. 463-491.
Status: Published
Toft, J. (2007). Wave front set for positive operators and for positive elements in non-commutative convolution algebras. Studia Mathematica. 179 (1). 63-80.
Status: Published
Toft, J. (2006). Positivity in twisted convolution algebra and Fourier modulation spaces. Bulletin de l'Académie serbe des sciences et des arts: Classe des sciences mathématiques et naturelles, sciences mathémathiques. 31. 75-86.
Status: Published
Toft, J. (2006). Fourier modulation spaces and positivity in twisted convolution algebra. Integral Transforms and Special Functions. 17 (02-03). 193-198.
Status: Published
Toft, J. (2006). Schatten-von Neumann Properties in the Weyl Calculus and Calculus of Metrics on Symplectic Vector Spaces. Annals of Global Analysis and Geometry. 30. 169-209.
Status: Published
Toft, J. (2005). Embeddings and compactness for generalized Sobolev-Shubin spaces and modulation spaces. Applicable Analysis. 84 (3). 269-282.
Status: Published
Toft, J. (2004). Minimization under entropy conditions, with applications in lower bound problems. Journal of Mathematical Physics. 45. 3216-3227.
Status: Published
Toft, J. (2004). Continuity properties for modulation spaces, with applications to pseudo-differential calculus, I. Journal of Functional Analysis. 207 (2). 399-429.
Status: Published
Toft, J. (2004). Continuity Properties for Modulation Spaces, with Applications to Pseudo-Differential Calculus, II. Annals of Global Analysis and Geometry. 26 (1). 73-106.
Status: Published
Toft, J. (2003). Positivity properties for noncommutative convolution algebras with applications in pseudo-differential calculus. Bulletin des Sciences Mathématiques. 127 (2). 101-132.
Status: Published
Toft, J. (2002). Continuity properties for non-commutative convolution algebras with applications in pseudo-differential calculus. Bulletin des Sciences Mathématiques. 126 (2). 115-142.
Status: Published
Toft, J. (2001). Subalgebras to a Wiener type Algebra of Pseudo-Differential operators. Annales de l'Institut Fourier. 51 (5). 1347-1383.
Status: Published
Toft, J. (2000). Regularizations, decompositions and lower bound problems in the Weyl calculus. Communications in Partial Differential Equations. 25 (7 & 8). 1201-1234.
Status: Published

Conference paper (Refereed)

Nordebo, S., Gustafsson, S., Ioannidis, A., Nilsson, B., Toft, J. (2013). On the generalized Jordan's lemma with applications in waveguide theory. Proceeding of 2013 URSI International Symposium on Electromagnetic Theory (EMTS) : International Conference Center Hiroshima, Hiroshima, Japan, May 20-24, 2013. 1039-1042.
Holst, A., Toft, J., Wahlberg, P. (2010). Weyl product algebras and classical modulation spaces. Linear and non-linear theory of generalized functions and its applications. 153-158.

Chapter in book (Refereed)

Teofanov, N., Toft, J. (2022). An Excursion to Multiplications and Convolutions on Modulation Spaces. Operator and Norm Inequalities and Related Topics. Springer. 601-637.
Abdeljawad, A., Toft, J. (2020). Anisotropic Gevrey-Hörmander Pseudo-Differential Operators on Modulation Spaces. Advances in Microlocal and Time-Frequency Analysis. Birkhäuser Verlag. 1-20.
Toft, J. (2020). Wiener Estimates on Modulation Spaces. Advances in Microlocal and Time-Frequency Analysis. Birkhäuser Verlag. 475-505.
Toft, J. (2019). Semi-continuous convolution estimates on weakly periodic Lebesgue spaces. Landscapes of Time-Frequency Analysis. Springer. 309-321.
Toft, J. (2017). Matrix parameterized pseudo-differential calculi on modulation spaces. Generalized functions and Fourier analysis : dedicated to Stevan Pilipović on the occasion of his 65th birthday. Springer. 215-235.
Chen, Y., Signahl, M., Toft, J. (2017). Hilbert space embeddings for Gelfand–Shilov and Pilipović spaces. Generalized Functions and Fourier Analysis : Dedicated to Stevan Pilipović on the Occasion of his 65th Birthday. Springer. 31-44.
Toft, J. (2015). Gabor Analysis for a Broad Class of Quasi-Banach Modulation Spaces. Pseudo-Differential Operators and Generalized Functions. Springer. 255-284.
Coriasco, S., Johansson, K., Toft, J. (2014). Global Wave-front Sets of Intersection and Union Type. Fourier Analysis : Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations. Heidelberg, New York, Dordrecht, London, Springer. 91-106.
Johansson, K., Pilipovic, S., Teofanov, N., Toft, J. (2013). A note on wave-front sets of Roumieu type ultradistributions. Pseudo-Differential Operators, Generalized Functionsand Asymptotics. Basel Heidelberg NewYork Dordrecht London, Springer. 239-252.
Toft, J. (2013). Multiplication properties in Gelfand-Shilov pseudo-differential calculus. Pseudo-Differential Operators, Generalized Functions and Asymptotics Operators Theory : Advances and Applications. Basel, Heidelberg, New York, Dordrecht, London, Birkhäuser Verlag. 117-172.
Pilipovic, S., Teofanov, N., Toft, J. (2011). Singular Support and FL^q Continuity of Pseudodifferential Operators. Approximation and Computation. Springer. 365-383.
Toft, J. (2010). Pseudo-differential operators with symbols in modulation spaces. Pseudo-Differential Operators : Complex Analysis and Partial Differential Equations. Basel, Birkhäuser Verlag. 223-234.
Toft, J. (2008). Schatten properties for pseudo-differential operators on modulation spaces. Pseudo-Differential Operators : Quantization and Signals. Springer, Berlin Heidelberg.
Toft, J., Buzano, E. (2007). Continuity and compactness properties of pseudo-differential operators. Pseudo-Differential Operators: Partial Differential Equations and Time-Frequency Analysis. Fields Institute Communications, American Mathematical Society,.
Toft, J. (2007). Continuity and Schatten Properties for Pseudo-Differential Operators on Modulation Spaces. Modern Trends in Pseudo-Differential Operators. Birkhäuser, Basel-Boston-Berlin. 173-206.
Toft, J. (2007). Continuity and Schatten Properties for Toeplitz Operators on Modulation Spaces. Modern Trends in Pseudo-Differential Operators. Birkhäuser, Basel-Boston-Berlin. 313-328.
Toft, J., Concetti, F. (2007). Trace ideals for Fourier integral operators with non-smooth symbols. Pseudo-Differential Operators: Partial Differential Equations and Time-Frequency Analysis. Fields Institute Communications, American Mathematical Society,.
Toft, J. (2006). Hudson's Theorem and Rank One Operators in Weyl Calculus. Pseudo-Differential Operators and Related Topics. Birkhäuser, Basel-Boston-Berlin.
Toft, J., Boggiatto, P. (2006). Non-stationary filters on modulation spaces. Mathematical modeling of wave phenomena. American Institute of Physics, Melville-New York. 361-368.

Collection (editor) (Refereed)

Pilipovic, S., Toft, J. (2015). Pseudo-Differential Operators and Generalized Functions. Heidelberg, New York, Dordrecht, London, Springer. 290.
Toft, J., Wong, M., Zhu, H. (2007). Modern Trends in Pseudo-Differential Operators. Birkhäuser, Basel-Boston-Berlin. 342.
Toft, J., Boggiatto, P., Rodino, L., Wong, M. (2006). Pseudo-Differential Operators and Related Topics. Birkhäuser, Basel-Boston-Berlin. 244 sidor.

Report (Other academic)

Ivanenko, Y., Gustafsson, M., Jonsson, B., Luger, A., Nilsson, B., et al. (2017). Passive approximation and optimization with B-splines. 24.
Toft, J., Concetti, F. (2007). Trace ideals for Fourier integral operators with non-smooth symbols. Växjö Universitet, Växjö. 13.
Toft, J., Wahlberg, P. (2006). Algebraic properties off the Weyl product on modulation spaces. Växjö Universitet, Växjö. 18.
Toft, J., Holst, A., Wahlberg, P. (2006). Modulation spaces and Weyl product algebras. Växjö Universitet, Växjö. 24.
Toft, J. (2006). Wave front set for positive operators and for positive elements in non-commutative convolution algebras. Växjö Universitet, Växjö. 15.

Conference proceedings (editor) (Other academic)

Toft, J. (2017). ISAAC Congress 2017 : 14-18 August 2017 Växjö, Sweden. Linnaeus university, Department of mathematics. 144.

Manuscript (preprint) (Other academic)

Coriasco, S., Johansson, K., Toft, J. Global wave front set of modulation space type.

Report (Other (popular science, discussion, etc.))

Toft, J., Boggiatto, P. (2006). Schatten classes for Toeplitz operators with Hilbert space windows on modulation spaces. Växjö Universitet, Växjö. 26.