This book contains a self-consistent treatment of Besov spaces for W*-dynamical systems,
based on the Arveson spectrum and Fourier multipliers. Generalizing classical results by …

We consider synthetic materials consisting of self-coupled identical resonators carrying
classical internal degrees of freedom. The architecture of such material is specified by the …

We introduce a notion of covolume for point sets in locally compact groups that
simultaneously generalizes the covolume of a lattice and the reciprocal of the Beurling …

We introduce a notion of weak anticommutativity for a pair (S, T) of self-adjoint regular
operators in a Hilbert C⁎-module E. We prove that the sum S+ T of such pairs is self-adjoint …

The bulk-boundary and a new bulk-defect correspondence principles are formulated using
groupoid algebras. The new strategy relies on the observation that the groupoids of lattices …

We consider the algebra Σ˙(L) generated by the inner-limit derivations over the GICAR
algebra of a fermion gas populating an aperiodic Delone set L. Under standard physical …

In space-adiabatic approaches one can approximate Hamiltonians that are modulated
slowly in space by phase-space functions that depend on position and momentum. In this …

Following the operator algebraic approach to Gabor analysis, we construct frames of
translates for the Hilbert space localisation of the Morita equivalence bimodule arising from …

A typical crystal is a finite piece of a material which may be invariant under some point
symmetry group. If it is a so-called intrinsic higher-order topological insulator or …

Topological phases of gapped one-particle Hamiltonians with (anti)-unitary symmetries are
classified by strong topological invariants according to the Altland-Zirnbauer table. Those …