Blar i Institutt for matematiske fag på tidsskrift "Journal of Fourier Analysis and Applications"
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A Duality Principle for Groups II: Multi-frames Meet Super-Frames
(Peer reviewed; Journal article, 2020)The duality principle for group representations developed in Dutkay et al. (J Funct Anal 257:1133–1143, 2009), Han and Larson (Bull Lond Math Soc 40:685–695, 2008) exhibits a fact that the well-known duality principle in ... -
Equivalent Norms for Modulation Spaces from Positive Cohen’s Class Distributions
(Peer reviewed; Journal article, 2022)We give a new class of equivalent norms for modulation spaces by replacing the window of the short-time Fourier transform by a Hilbert–Schmidt operator. The main result is applied to Cohen’s class of time-frequency ... -
Fourier Interpolation and Time-Frequency Localization
(Peer reviewed; Journal article, 2021)We prove that under very mild conditions for any interpolation formula f(x)=∑λ∈Λf(λ)aλ(x)+∑μ∈Mf^(μ)bμ(x) we have a lower bound for the counting functions nΛ(R1)+nM(R2)≥4R1R2−Clog2(4R1R2) which very closely matches recent ... -
Heisenberg modules as function spaces
(Peer reviewed; Journal article, 2020)Let \Delta be a closed, cocompact subgroup of G \times \widehat{G}, where G is a second countable, locally compact abelian group. Using localization of Hilbert C^*-modules, we show that the Heisenberg module \mathcal ... -
Mixed-State Localization Operators: Cohen’s Class and Trace Class Operators
(Journal article; Peer reviewed, 2019)We study mixed-state localization operators from the perspective of Werner’s operator convolutions which allows us to extend known results from the rank-one case to trace class operators. The idea of localizing a signal ... -
On a (No Longer) New Segal Algebra: A Review of the Feichtinger Algebra
(Journal article; Peer reviewed, 2018)Since its invention in 1979 the Feichtinger algebra has become a useful Banach space of functions with applications in time-frequency analysis, the theory of pseudo-differential operators and several other topics. It is ... -
Polyanalytic Toeplitz Operators: Isomorphisms, Symbolic Calculus and Approximation of Weyl Operators
(Peer reviewed; Journal article, 2021)We discuss an extension of Toeplitz quantization based on polyanalytic functions. We derive isomorphism theorem for polyanalytic Toeplitz operators between weighted Sobolev-Fock spaces of polyanalytic functions, which are ... -
A Primer on Coorbit Theory
(Peer reviewed; Journal article, 2021)Coorbit theory is a powerful machinery that constructs a family of Banach spaces, the so-called coorbit spaces, from well-behaved unitary representations of locally compact groups. A core feature of coorbit spaces is that ... -
Quantum Harmonic Analysis on Lattices and Gabor Multipliers
(Peer reviewed; Journal article, 2020)We develop a theory of quantum harmonic analysis on lattices in R2d. Convolutions of a sequence with an operator and of two operators are defined over a lattice, and using corresponding Fourier transforms of sequences and ... -
Spectral Invariance of ∗ -Representations of Twisted Convolution Algebras with Applications in Gabor Analysis
(Journal article; Peer reviewed, 2021)We show spectral invariance for faithful ∗-representations for a class of twisted convolution algebras. More precisely, if G is a locally compact group with a continuous 2-cocycle c for which the corresponding Mackey group ... -
Two types of Rubio de Francia operators on Triebel-Lizorkin and Besov spaces
(Peer reviewed; Journal article, 2018)We discuss generalizations of Rubio de Francia’s inequality for Triebel–Lizorkin and Besov spaces, continuing the research from Osipov (Sb Math 205(7): 1004–1023, 2014) and answering Havin’s question to one of the authors. ...