Patrik Wahlberg

Teaching

Courses in mathematics for students on engineering programs, master programs in engineering, bachelor and master programs in mathematics and physics, teacher training programs, and postgraduate courses.

Research

Pseudodifferential operators, microlocal analysis, harmonic analysis, and time-frequency analysis. Applications in linear partial differential equations, signal analysis and quantum mechanics.

Commissions

Director of the Applied Mathematics Programme.

Publications

Article in journal (Refereed)

Cappiello, M., Schulz, R., Wahlberg, P. (2020). Shubin type Fourier integral operators and evolution equations. Journal of Pseudo-Differential Operators and Applications. 11. 119-139.
Chen, Y., Toft, J., Wahlberg, P. (2019). The Weyl product on quasi-Banach modulation spaces. Bulletin of Mathematical Sciences. 9. 1-30.
Wahlberg, P. (2018). Propagation of polynomial phase space singularities for Schrödinger equations with quadratic Hamiltonians. Mathematica Scandinavica. 122. 107-140.
Pravda-Starov, K., Rodino, L., Wahlberg, P. (2018). Propagation of Gabor singularities for Schrödinger equations with quadratic Hamiltonians. Mathematische Nachrichten. 291. 128-159.
Cappiello, M., Schulz, R., Wahlberg, P. (2018). Conormal distributions in the Shubin calculus of pseudodifferential operators. Journal of Mathematical Physics. 59.
Carypis, E., Wahlberg, P. (2017). Propagation of exponential phase space singularities for Schrödinger equations with quadratic Hamiltonians. Journal of Fourier Analysis and Applications. 23. 530-571.
Schulz, R., Wahlberg, P. (2017). The Equality of the homogeneous and the Gabor wave front set. Communications in Partial Differential Equations. 42. 703-730.
Schulz, R., Wahlberg, P. (2016). Microlocal properties of Shubin pseudodifferential and localization operators. Journal of Pseudo-Differential Operators and Applications. 7. 91-111.
Cordero, E., Toft, J., Wahlberg, P. (2014). Sharp results for the Weyl product on modulation spaces. Journal of Functional Analysis. 267. 3016-3057.
Rodino, L., Wahlberg, P. (2014). The Gabor wave front set. Monatshefte für Mathematik (Print). 173. 625-655.
Cordero, E., Tabacco, A., Wahlberg, P. (2013). Schrodinger-type propagators, pseudodifferential operators and modulation spaces. Journal of the London Mathematical Society. 88. 375-395.
Oliaro, A., Rodino, L., Wahlberg, P. (2012). Almost periodic pseudodifferential operators and Gevrey classes. Annali di Matematica Pura ed Applicata. 191. 725-760.
Wahlberg, P., Schreier, P. (2012). On the instantaneous frequency of Gaussian stochastic processes. Probability and Mathematical Statistics. 32. 69-92.
Wahlberg, P. (2012). Representations of almost periodic pseudodifferential operators and applications in spectral theory. Journal of Pseudo-Differential Operators and Applications. 3. 81-119.
Boggiatto, P., Oliaro, A., Wahlberg, P. (2012). The wave front set of the Wigner distribution and instantaneous frequency. Journal of Fourier Analysis and Applications. 18. 410-438.
Toft, J., Wahlberg, P. (2012). Embeddings of alpha-modulation spaces. Pliska Studia Mathematica Bulgarica. 21. 25-46.
Wahlberg, P. (2011). Locally stationary stochastic processes and Weyl symbols of positive operators. Positivity (Dordrecht). 15. 105-134.
Wahlberg, P., Schreier, P. (2011). Locally stationary harmonizable complex improper stochastic processes. Journal of Time Series Analysis. 32. 33-46.
Wahlberg, P. (2010). Regularization of kernels for estimation of the Wigner spectrum of Gaussian stochastic processes. Probability and Mathematical Statistics. 30. 369-381.
Wahlberg, P., Schreier, P. (2010). On Wiener filtering of certain locally stationary stochastic processes. Signal Processing. 90. 885-890.
Wahlberg, P., Schreier, P. (2009). Gabor discretization of the Weyl product for modulation spaces and filtering of nonstationary stochastic processes. Applied and Computational Harmonic Analysis. 26. 97-120.
Wahlberg, P. (2009). A transformation of almost periodic pseudodifferential operators to Fourier multiplier operators with operator-valued symbols. Rendiconti del Seminario Matematico. 67. 247-269.
Wahlberg, P., Schreier, P. (2008). Spectral relations for multidimensional complex improper stationary and (almost) cyclostationary processes. IEEE Transactions on Information Theory. 54. 1670-1682.
Wahlberg, P. (2007). Vector-valued modulation spaces and localization operators with operator-valued symbols. Integral equations and operator theory. 59. 99-128.
Toft, J., Holst, A., Wahlberg, P. (2007). Weyl product algebras and modulation spaces. Journal of functional analysis. 251. 463-491.
Wahlberg, P., Hansson, M. (2007). Kernels and multiple windows for estimation of the Wigner-Ville spectrum of Gaussian locally stationary processes. IEEE Transactions on Signal Processing. 55. 73-84.
Wahlberg, P. (2005). The random Wigner distribution of Gaussian stochastic processes with covariance in S0(R2d). Journal of Function Spaces and Applications. 3. 163-181.
Wahlberg, P., Lantz, G. (2002). Approximate time-variable coherence analysis of multichannel signals. Multidimensional systems and signal processing. 13. 237-264.

Conference paper (Refereed)

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)

Wahlberg, P. (2020). The Gabor wave front set of compactly supported distributions. Advances in Microlocal and Time-Frequency Analysis. Birkhäuser Verlag. 507-520.
Wahlberg, P. (2006). The Wigner distribution of Gaussian weakly harmonizable stochastic processes. Pseudo-differential operators and related topics operator theory : Advances and Applications. Basel, Birkhäuser Verlag. 211-226.