Related papers: Products on Schatten-von Neumann classes and modul…
We deduce factorization properties for a quasi-Banach module over a quasi-Banach algebra. Especially we extend a result by Hewitt and prove that if any such algebra which possess a bounded left approximate identity, then any element in the…
We consider Schatten class membership of Hankel operators on Paley--Wiener spaces of convex $\Omega \subset \mathbb{R}^n$, both for bounded and unbounded domains. In particular, the classical product Hardy spaces fit within our theory. For…
We characterise the Schatten class $S^p$ properties of commutators $[b,T]$ of singular integrals and pointwise multipliers in a general framework of (quasi-)metric measure spaces. This covers, unifies, and extends a range of previous…
In this paper, we characterize invertible Toeplitz products on a number of Banach spaces of analytic functions, including weighted Bergman space $L^p_a (\mathbb{B}_n, dv_\gamma)$, the Hardy space $H^p(\partial \mathbb{D})$, and the weighted…
We consider multiplication properties of elements in weighted Fourier Lebesgue and modulation spaces. Especially we extend some results by Pilipovic, Teofanov and Toft (2010).
We extend the matrix representation of magnetic pseudo-differential operators in a tight Gabor frame from [arXiv:1804.05220, arXiv:2212.12229] to asymmetrical quantizations and smooth symbols dominated by a tempered weight (and not just…
We present a short proof of the fact that the Weyl quantisation of a tempered distribution with compactly supported Fourier transform is in the Schatten $p$-class if and only if the symbol is $L^p$-integrable. The proof is based on…
We consider nuclear function spaces on which the Weyl-Heisenberg group acts continuously and study the basic properties of the twisted convolution product of the functions with the dual space elements. The final theorem characterizes the…
We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…
We study Schatten--von Neumann properties of multiple operator integrals with integrands in the Haagerup tensor product of $L^\infty$ spaces. We obtain sharp, best possible estimates. This allowed us to obtain sharp Schatten--von Neumann…
This paper uses frame techniques to characterize the Schatten class properties of integral operators. The main result shows that if the coefficients of certain frame expansions of the kernel of an integral operator are in (\ell^{2,p}), then…
This note introduces a special class of tuples of bounded operators on a Hilbert space. It is called the Agler Young class. Major results about this class include a Wold decomposition and a dilation theorem. The structure of the dilation is…
We consider Fourier integral operators with symbols in modulation spaces and non-smooth phase functions whose second orders of derivatives belong to certain types of modulation space. We establish continuity and Schatten-von Neumann…
We consider Fourier integral operators with symbols in modulation spaces and non-smooth phase functions whose second orders of derivatives belong to certain types of modulation space. We establish continuity and Schatten-von Neumann…
We describe boundedness and compactness properties for the operators obtained by the Weyl-Pedersen calculus in the case of the irreducible unitary representations of nilpotent Lie groups that are associated with flat coadjoint orbits. We…
We provide a new and elementary proof of the continuity theorem for the wavelet and left-inverse wavelet transforms on the spaces $ \mathcal{S}_0(\mathbb{R}^n) $ and $ \mathcal{S}(\mathbb{H}^{n+1})$. We then introduce and study a new class…
We introduce a way of regarding Hilbert von Neumann modules as spaces of operators between Hilbert space, not unlike [Skei], but in an apparently much simpler manner and involving far less machinery. We verify that our definition is…
We define localized modulation maps and modulation spaces of symbols suited to the study of Rieffel's deformation quantization pseudodifferential calculus. They are used to generate Hilbert space representations for the quantized…
We define Schatten classes of adjointable operators on Hilbert modules over abelian $C^*$-algebras. Many key features carry over from the Hilbert space case. In particular, the Schatten classes form two-sided ideals of compact operators and…
This paper provides sufficient conditions for the boundedness of Weyl operators on modulation spaces. The Weyl symbols belong to Wiener amalgam spaces, or generalized modulation spaces, as recently renamed by their inventor Hans…