Related papers: Littlewood-type theorems for random Dirichlet seri…

The analysis of nonlocal discrete equations driven by fractional powers of the discrete Laplacian on a mesh of size $h>0$ \[ (-\Delta_h)^su=f, \] for $u,f:\mathbb{Z}_h\to\mathbb{R}$, $0<s<1$, is performed. The pointwise nonlocal formula for…

We establish an analogue of Wolff's theorem on ideals in $H^{\infty}(\mathbb{D})$ for the multiplier algebra of weighted Dirichlet space.

Let $\mathbb{B}^d$ be the unit ball on the complex space $\mathbb{C}^d$ with normalized Lebesgue measure $dv.$ For $\alpha\in\mathbb{R},$ denote $k_\alpha(z,w)=\frac{1}{(1-\langle z,w\rangle)^\alpha},$ the Bergman-type integral operator…

We give an elementary proof of an analogue of Fej\'er's theorem in weighted Dirichlet spaces with superharmonic weights. This provides a simple way of seeing that polynomials are dense in such spaces.

Using the Dirichlet theorem on the equidistribution of residue classes modulo $q$ and the Lemke Oliver-Soundararajan conjecture on the distribution of pairs of residues on consecutive primes, we show that the domain of convergence of the…

We consider the problem of embedding one i.i.d.\ collection of Bernoulli random variables indexed by $\mathbb{Z}^d$ into an independent copy in an injective $M$-Lipschitz manner. For the case $d=1$, it was shown by Basu and Sly (PTRF, 2014)…

In this article, we consider limit theorems for some weighted type random sums (or discrete rough integrals). We introduce a general transfer principle from limit theorems for unweighted sums to limit theorems for weighted sums via rough…

Following upon results of Putinar, Sun, Wang, Zheng and the first author, we provide models for the restrictions of the multiplication by a finite Balschke product on the Bergman space in the unit disc to its reducing subspaces. The models…

We provide a new version of the well-known Birkhoff-Kellogg invariant-direction Theorem in product spaces. Our results concern operator systems and give the existence of component-wise eigenvalues, instead of scalar eigenvalues as in the…

We show that in a scale of weighted Dirichlet spaces $D_{\alpha}$, including the Bergman space, given any finite Blaschke product $B$ there exists an equivalent norm in $D_{\alpha}$ such that $B$ satisfies the wandering subspace property…

In this paper, a family of holomorphic spaces of tent type in the unit ball of $\mathbb{C}^n$ is introduced, which is closely related to maximal and area integral functions in terms of the Bergman metric. It is shown that these spaces…

The article [HPS] established a monotonicity inequality for the Helmholtz equation and presented applications to shape detection and local uniqueness in inverse boundary problems. The monotonicity inequality states that if two scattering…

We consider cyclic $m$-isometries on a complex separable Hilbert space. Such operators are characterized in terms of shifts on abstract spaces of weighted Dirichlet type. Our results resemble those of Agler and Stankus, but our model spaces…

This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogonal polynomials in dependent random variables. Unlike the…

We prove that the Littlewood conjecture is satisfied for a restricted class of pairs $(\alpha,\beta)$ of badly approximable numbers. We use the localization of the roots of a cubic equation with coefficients depending on the diophantine…

We extend the method of layer potentials to manifolds with boundary and cylindrical ends. To obtain this extension along the classical lines, we have to deal with several technical difficulties due to the non-compactness of the boundary,…

In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also we study boundedness…

This note deals with a problem of the probabilistic Ramsey theory in functional analysis. Given a linear operator $T$ on a Hilbert space with an orthogonal basis, we define the isomorphic structure $\Sigma(T)$ as the family of all subsets…

For a general Dirichlet series $\sum a_n e^{-\lambda_n s}$ with frequency $\lambda=(\lambda_n)_n$, we study how horizontal translation (i.e. convolution with a Poisson kernel) improves its integrability properties. We characterize…

We give a sufficient condition for a composition operator with positive characteristic to be compact on the Hardy space of Dirichlet series.