相关论文: On the simultaneous Approximation of coefficients …

We study the behaviour of the smallest possible constants $d_n$ and $c_n$ in Hardy's inequalities $$ \sum_{k=1}^{n}\Big(\frac{1}{k}\sum_{j=1}^{k}a_j\Big)^2\leq d_n\,\sum_{k=1}^{n}a_k^2, \qquad (a_1,\ldots,a_n) \in \mathbb{R}^n $$ and $$…

Let $f$ be a holomorphic function on the unit disc, and $(S_{n_{k}})$ be a subsequence of its Taylor polynomials about $0$. It is shown that the nontangential limit of $f$ and lim$_{k\rightarrow \infty }S_{n_{k}}$ agree at almost all points…

We use techniques of proof mining to extract a uniform rate of metastability (in the sense of Tao) for the strong convergence of approximants to fixed points of uniformly continuous pseudocontractive mappings in Banach spaces which are…

Considering functions $ f $ on $ \R^n $ for which both $ f $ and $ \hat{f} $ are bounded by the Gaussian $ e^{-{1/2}a|x|^2}, 0 < a < 1 $ we show that their Fourier-Hermite coefficients have exponential decay. Optimal decay is obtained for $…

This paper focuses on estimating the Taylor coefficients for Hilbert spaces of holomorphic functions on the disk using intrinsic features of univalent functions and of Teichmuller spaces. Estimating these coefficients has a long history but…

We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.

In the present paper we introduce the notion of harmonicity modulus and harmonicity K-functional and apply these notions to prove a Jackson type theorem for approximation of continuous functions by polyharmonic functions. For corresponding…

By comparing a function and its $(k, \frac{2}{n})-$Fourier transform to a Gaussian analogue, $e^{-na|x|^\frac{2}{n}}$, we establish a Hardy-type uncertainty principle using Phragm\'en-Lindl\"of lemma. Furthermore, we investigate the heat…

The saturation theorem of [Knutson-Tao '99] concerns the nonvanishing of Littlewood-Richardson coefficients. In combination with work of [Klyachko '98], it implies [Horn '62]'s conjecture about eigenvalues of sums of Hermitian matrices.…

Strong convergence results on tamed Euler schemes, which approximate stochastic differential equations with superlinearly growing drift coefficients that are locally one-sided Lipschitz continuous, are presented in this article. The…

We show that the properties of the lower part of the spectrum of the Helmholtz equation for an heterogeneous system in a finite region in $d$ dimensions, where the solutions to the homogeneous problems are known, can be systematically…

Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…

Two different proofs for an inf-sup type representation formula (minimax formula) of the additive eigenvalues corresponding to first-order Hamilton-Jacobi equations are given for quasiconvex (level-set convex) Hamiltonians not necessarily…

In this paper we prove sharp Hardy inequalities by using Maximal function theory. Our results improve and extend the well-known results of G.Hardy \cite{Ha04}, T.Cazenave \cite {Ca03}, J.-Y.Chemin\cite {Ch06} and T.Tao\cite {TT06}.

This paper concerns extension of the classical Lagrange theorem, on the eventual periodicity of continued fraction expansions of quadratic surds, and the versions of it found in the literature in the case of complex numbers. In this…

We generalize the proof of Karamata's Theorem by the method of approximation by polynomials to the operator case. As a consequence, we offer a simple proof of \emph{uniform dual ergodicity} for a very large class of dynamical systems with…

It is be shown that the sequence of Bernstein polynomials for a function of several variables converges to this function uniformly along with every partial derivative of any order, provided that the latter derivative is well defined and…

We present variants of Goodstein's theorem that are equivalent to arithmetical comprehension and to arithmetical transfinite recursion, respectively, over a weak base theory. These variants differ from the usual Goodstein theorem in that…

A theorem of Henry Helson shows that for every ordinary Dirichlet series $\sum a_n n^{-s}$ with a square summable sequence $(a_n)$ of coefficients, almost all vertical limits $\sum a_n \chi(n) n^{-s}$, where $\chi: \mathbb{N} \to…

Let $M$ be a closed complex submanifold in ${\mathbb C}^N$ with the complete K\"ahler metric induced by the Euclidean metric. Several finiteness theorems on the $L^p$ Bergman space of holomorphic sections of a given Hermitian line bundle…