Related papers: Polynomial approach to cyclicity for weighted $\el…

The solutions of a kind of second-order homogeneous partial differential equation are called (real kernel) alpha-harmonic functions. The alpha-harmonic functions and their first-order partial derivative functions on unit disk are estimated…

We generalize a classical result by A.Macintyre and W.Rogosinski on best $H^p$--approximation in $L^p$ of rational functions. For each inner function $\theta$ we give a description of $H^p$--badly approximable functions in $\bar \theta…

We prove the property that a function is cyclic (resp., non-cyclic) is not preserved by norm convergence in Dirichlet-type spaces $D_\alpha$, and show how other significant quantities for cyclicity do remain preserved under the limit of…

Let $V$ be a complete discrete valuation ring with residue field $\mathbb{F}$. We define a cyclic homology theory for algebras over $\mathbb{F}$, by lifting them to free algebras over $V$, which we enlarge to tube algebras and complete…

We study common frequently hypercyclic vectors for countable families of weighted backward shifts acting on $\ell_p$ spaces, $1\leq p<\infty$. Using probabilistic techniques, we develop a general existence criterion, complemented by a…

We establish the first pointwise ergodic theorems along thin sets of prime numbers; a set with zero density with respect to the primes. For instance we will be able to achieve this with the Piatetski-Shapiro primes. Our methods will be…

The optimal $L^p \to L^q$ mapping properties for the (local) helical maximal function are obtained, except for endpoints. The proof relies on tools from multilinear harmonic analysis and, in particular, a localised version of the…

For a function $f$, continuous on a compact convex set $K$ and analytic in its interior we construct a sequence of almost optimal polynomials that converge with a geometric rate at points of analyticity of $f$.

Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…

We introduce polynomially weighted $\ell^p$-norms on the bar complex of a finitely generated group. We prove that, for groups of polynomial or exponential growth, the homology of the completed complex does not depend on the value of $p$ in…

An equivalent norm in the weighted Bergman space $A^p_\omega$, induced by an $\omega$ in a certain large class of non-radial weights, is established in terms of higher order derivatives. Other Littlewood-Paley inequalities are also…

Let $E$ be a closed subset of the unit circle of measure zero. Recently, Beise and M\"uller showed the existence of a function in the Hardy space $H^2$ for which the partial sums of its Taylor series approximate any continuous function on…

Let k be a commutative algebra with the field of the rational numbers included in k and let (E,p,i) be a cleft extension of A. We obtain a new mixed complex, simpler than the canonical one, giving the Hochschild and cyclic homologies of E…

We study approximation of the embedding $\ell_p^m \hookrightarrow \ell_q^m$, $1 \leq p < q \leq \infty$, based on randomized algorithms that use up to $n$ arbitrary linear functionals as information on a problem instance where $n \ll m$. By…

In a recent paper we used a basic decomposition property of polyanalytic functions of order $2$ in one complex variable to characterize solutions of the classical $\overline{\partial}$-problem for given analytic and polyanalytic data. Our…

Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…

We consider the problem of approximating an analytic function on a compact interval from its values at $M+1$ distinct points. When the points are equispaced, a recent result (the so-called impossibility theorem) has shown that the best…

We exploit the idea to use the maximal-entropy method, successfully tested in information theory and statistical thermodynamics, to determine approximating function's coefficients and squared errors' weights simultaneously as output of one…

This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm for a subspace. The optimization is realized by alternating minimizations of the…

We establish sharp $L^p$ integral mean estimates for $(\alpha,\beta)$-harmonic functions on the unit disk. Explicit bounds for the functions and their partial derivatives are obtained in terms of boundary data, by means of the associated…