Related papers: Gap Labelling for Almost Periodic Sturm-Liouville …
We give a construction of Gabor type frames for suitable separable subspaces of the non-separable Hilbert spaces $AP_2({\mathbb R})$ of almost periodic functions of one variable. Furthermore we determine a non-countable generalized frame…
The well-known Asplund theorem states that the inverse of a (possibly one-sided) band matrix $A$ is a Green matrix. In accordance with quasiseparable theory, such a matrix admits a quasiseparable representation in its rank-structured part.…
We consider groupoids on $\{1,2,..,d\}^\mathbb{N}$, cocycles and the counting measure as transverse function. We generalize results relating quasi-invariant probabilities with eigenprobabilities for the dual of the Ruelle operator. We…
In this paper, we introduce graceful and near graceful labellings of several families of windmills. In particular, we use Skolem-type sequences to prove (near) graceful labellings exist for windmills with $C_3$ and $C_4$ vanes, and infinite…
We develop the Ruelle transfer operator theory for Axiom A diffeomorphisms and construct Sinai-Ruelle-Bowen measures, carrying the symbolic spectral results of Part I [64] over to smooth dynamics through the Markov partition coding of Part…
In this paper, we prove the quasi-compactness of the Frobenius-Perron operator for a piecewise convex map $\tau$ with a countably infinite number of branches on the interval $I=[0,1]$. We establish that for high enough $n$ iterates of…
In this paper we focus on the almost-diagonalization properties of $\tau$-pseudodifferential operators using techniques from time-frequency analysis. Our function spaces are modulation spaces and the special class of Wiener amalgam spaces…
A less studied numerical characteristic of periodic orbits of area preserving twist maps of the annulus is the twist or torsion number, called initially the amount of rotation. It measures the average rotation of tangent vectors under the…
The paper deals with Sturm-Liouville-type operators with frozen argument of the form $\ell y:=-y''(x)+q(x)y(a),$ $y^{(\alpha)}(0)=y^{(\beta)}(1)=0,$ where $\alpha,\beta\in\{0,1\}$ and $a\in[0,1]$ is an arbitrary fixed rational number. Such…
The Liouville action for two--dimensional quantum gravity coupled to interacting matter contains terms that have not been considered previously. They are crucial for understanding the renormalization group flow and can be observed in recent…
We obtain a perturbative proof of localization for quasiperiodic operators on $\ell^2(\Z^d)$ with one-dimensional phase space and monotone sampling functions, in the regime of small hopping. The proof is based on an iterative scheme which…
We develop relative oscillation theory for general Sturm-Liouville differential expressions of the form \[ \frac{1}{r}\left(-\frac{\mathrm d}{\mathrm dx} p \frac{\mathrm d}{\mathrm dx} + q\right) \] and prove perturbation results and…
Based on Nijenhuis-Richardson bracket and bidegree on the cohomology complex for a Lie conformal algebra, we develop a twisting theory of Lie conformal algebras. By using derived bracket constructions, we construct $L_\infty$-algebras from…
We consider Schr\"odinger operators $H^h = (ih d+{\bf A})^* (ih d+{\bf A})$ with the periodic magnetic field ${\bf B}=d{\bf A}$ on covering spaces of compact manifolds. Under some assumptions on $\bf B$, we prove that there are arbitrarily…
We propose a definition of irregular vertex operators in the H3+ WZW model. Our definition is compatible with the duality [1] between the H3+ WZW model and Liouville theory, and we provide the explicit map between correlation functions of…
Given a Galois covering of complete spin manifolds where the base metric has PSC near infinity, we prove that for small enough epsilon > 0, the epsilon spectral projection of the Dirac operator has finite trace in the Atiyah von Neumann…
Liouville conformal field theory describes a random geometry that fluctuates around a deterministic one: the unique solution of the problem of finding, within a given conformal class, a Riemannian metric with prescribed scalar and geodesic…
We extend the spectral approach of S. Gou\"ezel for the vector-valued almost sure invariance principle (ASIP) to certain classes of non-stationary sequences with a weaker control over the behavior of the covariance matrices, assuming only…
The purpose of this paper is to study nonnegative self-adjoint extensions associated with singular Sturm-Liouville expressions with strictly positive minimal operators. We provide a full characterization of all possible nonnegative…
In the equation of motion approach to the two-time Green's functions, conventional Tyablikov-type truncation of the chain of equations is rather arbitrary and apt to violate the analytical structure of Green's functions. Here, we propose a…