6 papers
The filter of singularities in global anisotropic microlocal analysis
Luigi Rodino, Patrik Wahlberg
We define a filter of time-frequency anisotropic global singularities of phase space for tempered distributions. The filter contains information from the corresponding anisotropic…
Filtering of second order generalized stochastic processes corrupted by additive noise
Patrik Wahlberg
We treat the optimal linear filtering problem for a sum of two second order uncorrelated generalized stochastic processes. This is an operator equation involving covariance operato…
The Wigner distribution of Gaussian tempered generalized stochastic processes
Patrik Wahlberg
We define the Wigner distribution of a tempered generalized stochastic process that is complex-valued symmetric Gaussian. This gives a time-frequency generalized stochastic process…
Polynomially oscillatory multipliers on Gelfand-Shilov spaces
Alexandre Arias Junior, Patrik Wahlberg
We study continuity of the multiplier operator acting on Gelfand--Shilov spaces, where is a polynomial on of degree at least two with real coefficients.…
Propagation of singularities for anharmonic Schrödinger equations
Marco Cappiello, Luigi Rodino, Patrik Wahlberg
We consider evolution equations for two classes of generalized anharmonic oscillators and the associated initial value problem in the space of tempered distributions. We prove that…
Propagation of anisotropic Gabor singularities for Schrödinger type equations
Marco Cappiello, Luigi Rodino, Patrik Wahlberg
We show results on propagation of anisotropic Gabor wave front sets for solutions to a class of evolution equations of Schrödinger type. The Hamiltonian is assumed to have a real-v…