Related papers: Operator synthesis. I. Synthetic sets, bilattices …
We introduce and study the notion of reduced spectral synthesis, which unifies the concepts of spectral synthesis and uniqueness in locally compact groups. We exhibit a number of examples and prove that every non-discrete locally compact…
The second part of our work on operator synthesis deals with individual operator synthesis of elements in some tensor products, in particular in Varopoulos algebras, and its connection with linear operator equations. Using a developed…
In this paper we study closed subspaces of ultradifferentiable functions which are invariant under the differentiation operator. We propose a version of spectral synthesis which takes into account the presence of non-trivial differentiation…
Harmonic synthesis describes translation invariant linear spaces of continuous complex valued functions on locally compact abelian groups. The basic result due to L. Schwartz states that such spaces on the reals are topologically generated…
In this paper we show that spectral analysis implies spectral synthesis for arbitrary varieties on locally compact Abelian groups, which have no discrete subgroup of infinite torsion free rank..
We extend the notions of quantum harmonic analysis, as introduced in R. Werner's paper from 1984 (J. Math. Phys. 25(5)), to abelian phase spaces, by which we mean a locally compact abelian group endowed with a Heisenberg multiplier. In this…
In this note, we consider a class of composition operators on Lebesgue spaces with variable exponents over metric measure spaces. Taking advantage of the compatibility between the metric-measurable structure and the regularity properties of…
Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward-backward splitting…
In this paper we discuss applications of the geometric theory of composition operators on Sobolev spaces to the spectral theory of non-linear elliptic operators. The lower estimates of the first non-trivial Neumann eigenvalues of the…
We present other examples illustrating the operator-theoretic approach to invariant integrals on quantum homogeneous spaces developed by Kuersten and the second author. The quantum spaces are chosen such that their coordinate algebras do…
We study compactness and the Fredholm property for linear operators on coorbit spaces over locally compact abelian phase spaces. In contrast to previous works, we do not impose any countability assumptions on the underlying groups. Our…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded semidefinite perturbation is considered. A variant of the Davis-Kahan $ \sin2\Theta $ theorem from [SIAM J. Numer. Anal. 7 (1970), 1--46]…
We extend the results by Froelich and Spronk and Turowska on the connection between operator synthesis and spectral synthesis for A(G) to second countable locally compact groups G. This gives us another proof that one-point subset of G is a…
This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…
We use operator algebras and operator theory to obtain new result concerning Berezin quantization of compact K\"ahler manifolds. Our main tool is the notion of subproduct systems of finite-dimensional Hilbert spaces, which enables all…
We prove that a bounded linear Hilbert space operator has the unit circle in its essential approximate point spectrum if and only if it admits an orbit satisfying certain orthogonality and almost-orthogonality relations. This result is…
This monograph develops the theory of Besov spaces for abelian group actions on semifinite von Neumann algebras and then proves Peller criteria for traceclass properties of associated Hankel operators. This allows to extend known index…
We give a systematic local description of invariant metrics and other invariant fields on a spacetime under the action of a (non-abelian) group. This includes the invariant fields in a neighbourhood of a principal and a special orbit. The…
We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend…
We study the spectral convergence of compact, self-adjoint operators on a separable Hilbert space under operator norm perturbations, and derive asymptotic expansions for their eigenvalues and eigenprojections. Our analysis focuses on…