Related papers: Simple Spectrum for Tensor Products of Mixing Map …

We consider quenched random perturbations of skew products of rotations on the unit circle over uniformly expanding maps on the unit circle. It is known that if the skew product satisfies a certain condition (shown to be generic in the case…

Let $\otimes$ be the map which classifies the tensor product of two line bundles, an extension of this map to the space of all codimension 1 algebraic cycles is constructed. It is proved that this extension cannot exist in codimension…

Let $G$ be a connected semisimple Lie group with finite centre, and let $M= \Gamma \backslash G$ be a compact homogeneous manifold. Under a spectral gap assumption, we show that smooth time-changes of any unipotent flow on $M$ have…

Given a map of simplicial topological spaces, mild conditions on degeneracies and the levelwise maps imply that the geometric realization of the simplicial map is a cofibration. These conditions are not formal consequences of model category…

By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…

We established two-sided Curto-Herrero conjecture for pairs of matrices, where the first matrix has a simple spectrum. Namely, it is shown that these pairs are separated by ranks of non-commutative polynomials in matrices. Moreover, we…

We show a precise proof of Steenbrink's formula for the spectrum of convenient Newton non-degenerate functions, and prove the symmetry of combinatorial polynomials in the simplicial case. Combined with the modified Steenbrink conjecture for…

It is shown that for every $\alpha$, where $\alpha\in [0, 1/2]$, there exists an $\alpha$-rigid transformation whose spectrum has Lebesgue component. This answers the question posed by Klemes and Reinhold in [7]. We apply a certain…

Ordinary maps satisfy topological recursion for a certain spectral curve $(x, y)$. We solve a conjecture from arXiv:1710.07851 that claims that fully simple maps, which are maps with non self-intersecting disjoint boundaries, satisfy…

We show that a spectrum of frequencies obtained by a random perturbation of the integers allows one to represent any measurable function on R by an almost everywhere converging sum of harmonics almost surely.

A mixing flow with homogeneous spectrum of multiplicity 2 is presented.

The spectrum of Hamiltonian (Markov matrix) of a multi-species asymmetric simple exclusion process on a ring is studied. The dynamical exponent concerning the relaxation time is found to coincide with the one-species case. It implies that…

In this note, we extend results about unique $n^{\textrm{th}}$ roots and cancellation of finite disconnected graphs with respect to the Cartesian, the strong and the direct product, to the rooted hierarchical products, and to a modified…

This article is a fundamental study in computable analysis. In the framework of Type-2 effectivity, TTE, we investigate computability aspects on finite and infinite products of effective topological spaces. For obtaining uniform results we…

The main objects under consideration in this thesis are called maps, a certain class of graphs embedded on surfaces. Our problems have a powerful relatively recent tool in common, the so-called topological recursion (TR) introduced by…

This paper is concerned with the prime spectrum of a tensor product of algebras over a field. It seeks necessary and sufficient conditions for such a tensor product to have the S-property, strong S-property, and catenarity. Its main results…

We consider smooth flows preserving a smooth invariant measure, or, equivalently, locally Hamiltonian flows on compact orientable surfaces and show that almost every such locally Hamiltonian flow with only simple saddles has singular…

For every natural $n>1$, there is an operator $T$ of dynamical origin such that its tensor power $T^{\otimes n}$ has singular spectrum, and $T^{\otimes (n+1)}$ has absolutely continuous one. For a set $D$ of positive measure there are…

We consider certain matrix-products where successive matrices in the product belong alternately to a particular qualitative class or its transpose. The main theorems relate structural and spectral properties of these matrix-products to the…

It is shown that if $E$ is any subset of $\Bbb N$ such that either $1\in E$ or $2\in E$ then there is a mixing transformation whose set of spectral multiplicities is $E$.