Related papers: New spectral multiplicities for mixing transformat…

Let $E$ be a subset of positive integers such that $E\cap\{1,2\}\ne\emptyset$. A weakly mixing finite measure preserving flow $T=(T_t)_{t\in\Bbb R}$ is constructed such that the set of spectral multiplicities (of the corresponding Koopman…

Each subset $E\subset\Bbb N$ is realized as the set of essential values of the multiplicity function for the Koopman operator of an ergodic conservative infinite measure preserving transformation.

It is shown that each subset of positive integers that contains 2 is realizable as the set of essential values of the multiplicity function for the Koopman operator of some weakly mixing transformation.

We introduce high staircase infinite measure preserving transformations and prove that they are mixing under a restricted growth condition. This is used to (i) realize each subset $E\subset\Bbb N\cup\{\infty\}$ as the set of essential…

We say that a semigroup of matrices has a submultiplicative spectrum if the spectrum of the product of any two elements of the semigroup is contained in the product of the two spectra in question (as sets). In this note we explore an…

We define a bijection that transforms an alternating sign matrix A with one -1 into a pair (N,E) where N is a (so called) ``neutral'' alternating sign matrix (with one -1) and E is an integer. The bijection preserves the classical…

This paper introduces and studies the Ehrhart spectrum of a set $E \subseteq \mathbb{Z}^r$, defined as the set of all Ehrhart polynomials of simplices with vertices in $E$, generalizing the notion of volume spectrum. We show that for any $E…

We introduce algebraic sets in the complex projective spaces for the mixed states in bipartite quantum systems as their invariants under local unitary operations. The algebraic sets of the mixed state have to be the union of the linear…

We obtain sequences of inclusion sets for the spectrum, essential spectrum, and pseudospectrum of banded, in general non-normal, matrices of finite or infinite size. Each inclusion set is the union of the pseudospectra of certain…

We introduce algebraic sets in the products of complex projective spaces for the mixed states in multipartite quantum systems as their invariants under local unitary operations. The algebraic sets have to be the union of the linear…

A bounded set $\Omega \subset \mathbb{R}^d$ is called a spectral set if the space $L^2(\Omega)$ admits a complete orthogonal system of exponential functions. We prove that a cylindric set $\Omega$ is spectral if and only if its base is a…

In this note we give an example of an ergodic non-singular map whose unitary operator admits a Lebesgue component of multiplicity one in its spectrum.

For totally ergodic Z^2-actions a collection of weak limits provide the set {2,4, ..., 2 ^ n} of spectral multiplicities for their tensor product. Our conditions allow to obtain a similar result for mixing actions via some limit procedure.

In this article we show that $\mathbb{S}/8$ is an $\mathbb{E}_1$-algebra, $\mathbb{S}/32$ is an $\mathbb{E}_2$-algebra, $\mathbb{S}/p^{n+1}$ is an $\mathbb{E}_n$-algebra at odd primes and, more generally, for every $h$ and $n$ there exist…

The interpretation of the existing experimental evidences for oscillations of neutrinos in schemes with three and four neutrino mixing is reviewed. Forms of the lepton mixing matrix allowed by the neutrino oscillation data are considered.…

A class of spectral problems with a hidden Lie-algebraic structure is considered. We define a duality transformation which maps the spectrum of one quasi-exactly solvable (QES) periodic potential to that of another QES periodic potential.…

We introduce a class of rank-one transformations, which we call extremely elevated staircase transformations. We prove that they are measure-theoretically mixing and, for any $f : \mathbb{N} \to \mathbb{N}$ with $f(n)/n$ increasing and…

In this paper, by providing a class of coherence measures in finite dimensional systems, a sufficient and necessary condition for the existence of coherence transformations that convert one probability distribution of any pure states into…

Let $G = (X, Y; E)$ be a bipartite graph with two vertex partition subsets $X$ and $Y$. $G$ is said to be balanced if $|X| = |Y|$. $G$ is said to be bipancyclic if it contains cycles of every even length from $4$ to $|V(G)|$. In this note,…

We prove that a rank one transformation satisfying a condition called restricted growth is a mixing transformation if and only if the spacer sequence for the transformation is uniformly ergodic. Uniform ergodicity is a generalization of the…