Related papers: A reconstruction theorem for almost-commutative sp…
We extend to twisted spectral triples the fluctuations of the metric, as well as their gauge transformations. The former are bounded perturbations of the Dirac operator that arise when a spectral triple is exported between Morita equivalent…
We generalize the notion of Gelfand triples (also called Banach-Gelfand triples or rigged Hilbert spaces) by dropping the necessity of a continuous embedding. This means in our setting we lack of a chain inclusion. We replace the continuous…
It is proved recently by Benamara-Nikolski that a contraction having finite defects and spectrum not filling in the closed unit disc, is similar to a normal operator if and only if it has the so-called linear resolvent growth property. We…
When aiming to apply mathematical results of non-commutative geometry to physical problems the question arises how they translate to a context in which only a part of the spectrum is known. In this article we aim to detect when a…
In this paper, we observe new phenomena related to the structure of 3-manifolds satisfying lower scalar curvature bounds. We construct warped-product manifolds of almost nonnegative scalar curvature that converge to pulled string spaces in…
In this paper we give a new prove of hyperbolicity of renormalization of critical circle maps using the formalism of almost-commuting pairs. We extend renormalization to two-dimensional dissipative maps of the annulus which are small…
Let M be a closed, orientable, irreducible, non-simply connected 3-manifold. We prove that if M admits a sequence of Riemannian metrics whose sectional curvature is locally controlled and whose thick part becomes asymptotically hyperbolic…
In the abstract pseudodifferential setup of Connes and Moscovici, we prove a general formula for the discrepancies of zeta-regularised traces associated with certain spectral triples, and we introduce a canonical trace on operators, whose…
We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage of the recurrence relations satisfied by the entries of such…
This paper addresses the reconstruction of periodic structures using phase or phaseless near-field measurements. We introduce a novel illumination strategy based on the quasi-periodic condition. Employing the Dirichlet-to-Neumann (DtN) map,…
Spectral reconstruction is a well studied numerically ill-posed problem which arises due to the relation of the Euclidean correlator to the spectral function via an inhomogeneous Fredholm equation of the first kind. Several different…
We propose a systematic scheme for computing the variation of rearrangement operators arising in the recently developed spectral geometry on noncommutative tori and $\theta$-deformed Riemannian manifolds. It can be summarized as a category…
In this short communication, we examine the relevance of the signature of the space-time metric in the construction of the product of a pseudo-Riemannian spectral triple with a finite triple describing the internal geometry. We obtain…
This paper treatises the preservation of some spectra under perturbations not necessarily commutative and generalizes several results which have been proved in the case of commuting operators.
Given a bigraded exact couple of modules over some ring, we determine the meaning of the $E^{\infty}$-terms of its associated spectral sequence: Let $L^{\ast}$ and $L_{\ast}$ denote the limit and colimit abutting objects of the exact…
An exact semiclassical version of the classical KAM theorem about small perturbations of vector fields on the torus is given. Moreover, a renormalization theorem based on counterterms for some semiclassical systems that are close to being…
A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The construction begins with a harmonic approximation of the…
The analog of the Chern-Gauss-Bonnet theorem is studied for a $C^*$-dynamical system consisting of a $C^*$-algebra $A$ equipped with an ergodic action of a compact Lie group $G$. The structure of the Lie algebra $\mathfrak{g}$ of $G$ is…
In the setting of non-type $\ty{II_1}$ representations, we propose a definition of {\it deformed Fredholm module} $\big[D_\ct|D_\ct|^{-1}\,,\,{\bf\cdot}\,\big]_\ct$ for a modular spectral triple $\ct$, where $D_\ct$ is the deformed Dirac…
We formulate conditions for almost-commutative (spacetime) manifolds under which the asymptotically expanded spectral action is renormalizable. These conditions are of a graph-theoretical nature, involving the Krajewski diagrams that…