arXiv subjects

Naim L. Braha

Publications and source records attributed to Naim L. Braha.

3 recordsLinked to original sources

arXiv2026

Complete asymptotic expansion for a Durrmeyer variant of operators based on Hermite polynomials

In this paper, we study a Durrmeyer variant of the positive linear operators based on two-variable Hermite polynomials recently introduced by G. Krech (2016). Our main objective is to establish a complete asymptotic expansion for these operators as n tends to infinity for locally integrable functions of polynomial growth. The coefficients of the expansion are explicitly expressed in terms of the derivatives of the function. As a corollary, a Voronovskaja-type formula is obtained.

math.CA↗

arXiv2023

Banach spaces of sequences arising from infinite matrices

Given an infinite matrix $M=(m_{nk})$ we study a family of sequence spaces $\ell_M^p$ associated with it. When equipped with a suitable norm $\|\cdot\|_{M,p}$ we prove some basic properties of the Banach spaces of sequences $(\ell_M^p,\|\cdot\|_{M,p})$. In particular we show that such spaces are separable and strictly/uniformly convex for a considerably large class of infinite matrices $M$ for all $p>1$. A special attention is given to the identification of the dual space $(\ell_M^p )^*$. Building on the earlier works of Bennett and Jägers, we extend and apply some classical factorization results to the sequence spaces $\ell_M^p$.

math.FA↗

arXiv2022

On Nörlund summability of Taylor series in weighted Dirichlet spaces

In this note we show that the Taylor series of a function in a weighted Dirichlet space is (generalized) Nörlund summable, provided that the sequence determining the Nörlund operator is non-decreasing and has finite upper growth rate. In particular the Taylor series is Nörlund summable for all $α>1/2$, and the rate of convergence is of the order $O(n^{-1/2})$. The inequality $α>1/2$ is sharp. On the other hand if the Taylor series is Nörlund summable and the partial sums of the determining sequence enjoy a certain growth condition then the determining sequence has finite lower growth rate. An analogue result is derived for a non-increasing sequence that is uniformly bounded away from zero.

math.FA↗