Related papers: Spectral triples from stationary Bratteli diagrams

A concise overview of the spectral theory of integral-functional operators is provided. In the context of analysis, a technique is described for deriving solutions to equations involving operators in a closed form. A constructive theorem…

In this article, we give an explicit description of the invertible functions on the Drinfeld symmetric space over $K$ a finite extension of $\mathbb{Q}_p$. We identify them with some distribution spaces over the profinite set of…

Let $\Gamma_n$ denote the $n$-th level Sierpi\'nski graph of the Sierpi\'nski gasket $K$. We consider, for any given conductance $(a_0, b_0, c_0)$ on $\Gamma_0$, the Dirchlet form ${\mathcal E}$ on $K$ obtained from a recursive construction…

It has been a long-standing open problem to construct a general framework for relating the spectra of dual theories to each other. Here, we solve this problem for the case of one-dimensional quantum lattice models with symmetry-twisted…

We classify and construct all real spectral triples over noncommutative Bieberbach manifolds, which are restrictions of irreducible real equivariant spectral triple over the noncommutative three-torus. We show that in the classical case the…

We construct symmetric self-similar Dirichlet forms on unconstrained Sierpinski carpets, which are natural extension of planar Sierpinski carpets by allowing the small cells to live off the $1/k$ grids. The intersection of two cells can be…

We provide a general framework for the realization of powers or functions of suitable operators on Dirichlet spaces. The first contribution is to unify the available results dealing with specific geometries; a second one is to provide new…

We derive a number of spectral results for Dirac operators in geometrically nontrivial regions in $\mathbb{R}^2$ and $\mathbb{R}^3$ of tube or layer shapes with a zigzag type boundary using the corresponding properties of the Dirichlet…

Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions…

It is well-known that characters classify linear representations of finite groups, that is if characters of two representations of a finite group are the same, these representations are equivalent. It is also well-known that, in general,…

We study the spectral approximation of a second-order elliptic differential eigenvalue problem that arises from structural vibration problems using isogeometric analysis. In this paper, we generalize recent work in this direction. We…

We consider four-dimensional $\mathcal{N}=1$ supergravity models of a kind appearing in string flux compactifications. It has been recently shown that, by using double three-form multiplets instead of ordinary chiral multiplets, one can…

Making use of a unified approach to certain classes of induced representations, we establish here a number of detailed spectral theoretic decomposition results. They apply to specific problems from non-commutative harmonic analysis, ergodic…

This paper provides sharp Dirichlet heat kernel estimates in inner uniform domains, including bounded inner uniform domains, in the context of certain (possibly non-symmetric) bilinear forms resembling Dirichlet forms. For instance, the…

We study spectral measures generated by infinite convolution products of discrete measures generated by Hadamard triples, and we present sufficient conditions for the measures to be spectral, generalizing a criterion by Strichartz. We then…

We explicitly construct Fredholm modules and spectral triples representing any element of $K$-homology groups of Hensel-Steinitz algebras.

This article gives a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate…

We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. The construction starts with a positive selfadjoint operator $H$, that is called the Hamiltonian of the…

We study isospectrality for manifolds with mixed Dirichlet-Neumann boundary conditions and express the well-known transplantation method in graph- and representation-theoretic terms. This leads to a characterization of transplantability in…

In this paper, we focus on strongly local regular Dirichlet forms, especially those satisfying Morrey-type inequalities. We prove the equivalence between resistance estimates and heat kernel estimates in this case. Self-similar forms on…