Related papers: Combining Riesz bases

Let B be a unital commutative semi-simple Banach algebra. We study endomorphisms of B which are simultaneously Riesz operators. Clearly compact and power compact endomorphisms are Riesz. Several general theorems about Riesz endomorphisms…

Walsh has recently proved the norm convergence of all nonconventional ergodic averages involving polynomial sequences in discrete nilpotent acting groups. He deduces this convergence from an equivalent, `finitary' assertion of stability…

In this paper we show the stability of the ball as maximizer of the Riesz potential among sets of given volume. The stability is proved with sharp exponent $1/2$, and is valid for any dimension $N\geq 2$ and any power $1<\alpha<N$.

Despite the recent advances in the theory of exponential Riesz bases, it is yet unknown whether there exists a set $S \subset \mathbb{R}^d$ which does not admit a Riesz spectrum, meaning that for every $\Lambda \subset \mathbb{R}^d$ the set…

We prove that the finite generation of adjoint rings proved in [Cascini and Lazi\'c] implies all the foundational results of the Minimal Model Program: the Rationality, Cone and Contraction theorems, the existence of flips, and termination…

A bounded, Riemann integrable and measurable set $K\subset \mathbb{R}^d$, which fulfills \[\sum\limits_{\gamma\in\Gamma}\mathbb{1}_K(x-\gamma)=k\text{ almost everywhere, $x\in\mathbb{R}^d$}\] for a lattice $\Gamma\subset\mathbb{R}^d$ is…

In this note we prove that single-conclusion admissible rules of any proper axiomatic extension of the infnite valued Lukasiewicz logic are finitely based.

We prove that if the neutral component in a finitely-generated associative algebra graded by a finite group has a Shirshov base, then so does the whole algebra.

We consider a finite number of orientation preserving $C^2$ interval diffeomorphisms and apply them randomly in such a way that the expected Lyapunov exponents at the boundary points are positive. We prove the exponential decay of…

We show that the points that converge to infinity under iteration of the exponential map form a connected subset of the complex plane.

Let $\lambda$ be a positive number, and let $(x_j:j\in\mathbb Z)\subset\mathbb R$ be a fixed Riesz-basis sequence, namely, $(x_j)$ is strictly increasing, and the set of functions $\{\mathbb R\ni t\mapsto e^{ix_jt}:j\in\mathbb Z\}$ is a…

For compact sets in Euclidean space, Riesz energies whose exponents differ by $1$ are shown to arise as the endpoint cases of a one-parameter family of infinite-strip energies as the strip thickness increases from $0$ to $\infty$, under…

In this paper, an equivalence between existence of particular exponential Riesz bases for multivariate bandlimited functions and existence of certain polynomial interpolants for these bandlimited functions is given. For certain classes of…

We prove that for every integer $d \ge 2$ there exists a dense collection of subsets of $[n]^d$ such that no two of them have a symmetric difference that may be written as the $d$th power of a union of at most $\lfloor d/2 \rfloor$…

We prove that every partially ordered simple group of rank one which is not Riesz embeds into a simple Riesz group of rank one if and only if it is not isomorphic to the additive group of the rationals. Using this result, we construct…

In this paper we explicitly compute finite bases of disjunctive identities and finite bases of regular representations for a number of interesting finite groups.

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

The paper is devoted to continuous frames and Riesz bases in Hilbert C*-modules. we define a continuous Riesz basis for Hilbert C*-modules and give some results about them.

We prove pointwise estimates to the modified Riesz potential. We show the boundedness of its Luxemburg norm. As an application we obtain Orlicz embedding results. We study the sharpness of the results.

The purpose of this note is to verify that the results attained in [6] admit an extension to the multidimensional setting. Namely, for subsets of the two dimensional torus we find the sharp growth rate of the step(s) of a generalized…