Related papers: The operator Fejer-Riesz theorem

In this paper, we give direct theorems on point wise and global approximation by new variants of Bernstein-Durrmeyer operator, introduced by A.-M. et al.[1].

Taylor's theorem (and its variants) is widely used in several areas of mathematical analysis, including numerical analysis, functional analysis, and partial differential equations. This article explains how Taylor's theorem in its most…

A decomposition theorem for self-adjoint operators proved by Riesz and Lorch is extended to normal operators. This extension gives a new proof of the spectral theorem for unbounded normal operators.

In 2001, M.Rekos described the analytic behavior for a function $f(z)$ connected with the Euler totient function for Im$z > 0$ (see (1.2)) imitating the previous research of [1] and [3]. In the present paper, for Im$z > 0$ we describe the…

We study superharmonic functions for Schr\"odinger operators on general weighted graphs. Specifically, we prove two decompositions which both go under the name Riesz decomposition in the literature. The first one decomposes a superharmonic…

We give a characterization of compact and Fredholm operators on polyanalytic Fock spaces in terms of limit operators. As an application we obtain a generalization of the Bauer-Isralowitz theorem using a matrix valued Berezin type transform.…

We collect and organise known results and add some new ones of the following nature: if A is a bounded operator in a Hilbert or Banach space, does there exist a nonconstant polynomial p(z) such that p(A) is "simpler", "nicer" than A. The…

A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are given for the boundedness of the operators under consideration…

In this paper, a new concept, the fuzzy rate of an operator in linear spaces is proposed for the very first time. Some properties and basic principles of it are studied. Fuzzy rate of an operator $B$ which is specific in a plane is…

We establish a connection between the ratios conjecture for the Riemann zeta-function and a conjecture concerning correlations of convolutions of M\"{o}bius and divisor functions. Specifically, we prove that the ratios conjecture and an…

This note is a complement to Pusz--Woronowicz's works on functional calculus for two positive forms from the viewpoint of operator theory. Based on an elementary, self-contained and purely Hilbert space operator explanation of their…

We generalize Lindeberg's proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables. The result is applied to get a similar theorem for smooth functions…

The purpose of this paper is to make an introduction to univalent function theory for readers of any level, assuming only foundational knowledge in real and complex analysis. In particular, we state and proof (with details) important…

Riemann sums, a classical method for approximating the definite integral of a function, have been extensively studied in the past. However, their monotonic properties, while still of great importance, particularly in approximation theory…

The Schinzel hypothesis is a famous conjectural statement about primes in value sets of polynomials, which generalizes the Dirichlet theorem about primes in an arithmetic progression. We consider the situation that the ring of integers is…

We consider a generalization of the Riesz operator in $R^d$ and obtain estimates for its norm and for related capacities via the modified Wolff potential. These estimates are based on the certain version of $T1$ theorem for…

We extend some definitions and give new results about the theory of slice analysis in several quaternionic variables. The sets of slice functions which are respectively slice, slice regular and circular w.r.t. given variables are…

Based on the Gale-Ryser theorem for the existence of suitable $(0,1)$-matrices for different partitions of a natural number, we revisit the classical result of G. G. Lorentz regarding the characterization of a plane measurable set, in terms…

We prove a generalized Birman-Schwinger principle in the non-self-adjoint context. In particular, we provide a detailed discussion of geometric and algebraic multiplicities of eigenvalues of the basic operator of interest (e.g., a…

We generalize Roe's index theorem for graded generalized Dirac operators on amenable manifolds to multigraded elliptic uniform pseudodifferential operators. The generalization will follow from a local index theorem that is valid on any…