Browsing Institutt for matematiske fag by Author "Knutsen, Helge"
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Daubechies' time-frequency localization operator on Cantor type sets II
Knutsen, Helge (Peer reviewed; Journal article, 2022)We study a version of the fractal uncertainty principle in the joint time-frequency representation. Namely, we consider Daubechies' localization operator projecting onto spherically symmetric n-iterate Cantor sets with an ... -
A fractal uncertainty principle for the short-time Fourier transform and Gabor multipliers
Knutsen, Helge (Peer reviewed; Journal article, 2023)We study the fractal uncertainty principle in the joint time-frequency representation, and we prove a version for the Short-Time Fourier transform with Gaussian window on the modulation spaces. This can equivalently be ... -
Norms and Eigenvalues of Time-Frequency Localization Operators
Knutsen, Helge (Master thesis, 2018)In this report we study and compare two types of time-frequency localization operators, the first is based on composition of projections in time and frequency, and the second is Daubechies' localization operator. We provide ... -
Uncertainty Principles in Time-Frequency Analysis – Fractals and Schrödinger Evolutions
Knutsen, Helge (Doctoral theses at NTNU;2023:162, Doctoral thesis, 2023)In this thesis we study two uncertainty principles from the perspective of timefrequency analysis. The first part, to which a significant portion is dedicated, is concerned with deriving an analog in the joint time-frequency ...