Related papers: A spectrum associated with Minkowski diagonal cont…

We formalise the undecidability of solvability of Diophantine equations, i.e. polynomial equations over natural numbers, in Coq's constructive type theory. To do so, we give the first full mechanisation of the…

For a positive measure set of nonuniformly expanding quadratic maps on the interval we effect a multifractal formalism, i.e., decompose the phase space into level sets of time averages of a given observable and consider the associated {\it…

In this paper, a multi-dimensional fractional wave equation that describes propagation of the damped waves is introduced and analyzed. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional…

In this paper we develop the convergence theory of simultaneous, inhomogeneous Diophantine approximation on manifolds. A consequence of our main result is that if the manifold $M \subset \mathbb{R}^n$ is of dimension strictly greater than…

In this paper we compute the spectrum, in the sense of Berkovich, of an ultrametric linear differential equation with constant coefficients, defined over an affinoid domain of the analytic affine line $A_k^{1,an}$. We show that it is a…

We present a deformation of the Minkowski space as embedded into the conformal space (in the formalism of twistors) based in the quantum versions of the corresponding kinematic groups. We compute explicitly the star product, whose Poisson…

In this paper we recall some results and some criteria on the convergence of matrix continued fractions. The aim of this paper is to give some properties and results of continued fractions with matrix arguments. Then we give continued…

We show that the spectrum of the complex Laplacian on a product of hermitian manifolds is the Minkowski sum of the spectra of the complex Laplacians on the factors. We use this fact to show that the range of the d-bar operator on a product…

In this paper, we derive the expression for spectral dimension using a modified diffusion equation in the kappa-deformed space-time. We start with the Beltrami-Laplace operator in the kappa-Minkowski space-time and obtain the deformed…

We prove new results on the derivative of the Minkowski question mark function. Some of our theorems are non-improvable.

We prove that for conformal expanding maps the return time does have constant multifractal spectrum. This is the counterpart of the result by Feng and Wu in the symbolic setting.

We relate the notions of spectral gap for unitary representations and subfactors with definability of certain important sets in the corresponding structures. We give several applications of this relationship.

Using the spectral theory of weakly convergent sequences of finite graphs, we prove the uniform existence of the integrated density of states for a large class of infinite graphs.

We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.

Mathematical diffraction theory is concerned with the analysis of the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and…

Classical results on Diophantine approximation, such as Roth's theorem, provide the most effective techniques for proving the transcendence of special kinds of continued fractions. Multidimensional continued fractions are a generalization…

The relation between densities of cycles and the spectrum of a graphon, which implies that the spectra of convergent graphons converge, fundamentally relies on the self-adjointness of the linear operator associated with a graphon. In this…

We construct a spectral sequence converging to symplectic homology of a Lefschetz fibration whose E1 page is related to Floer homology of the monodromy symplectomorphism and its iterates. We use this to show the existence of fixed points of…

By generalising Rudin's construction of an aperiodic sequence, we derive new substitution-based structures which have purely absolutely continuous diffraction and mixed dynamical spectrum, with absolutely continuous and pure point parts. We…

This paper is concerned with the study of diagonal Diophantine inequalities of fractional degree $ \theta ,$ where $ \theta >2$ is real and non-integral. For fixed non-zero real numbers $ \lambda_i $ not all of the same sign we write…