Related papers: Optimality of generalized Bernstein operators
We prove that, under certain assumptions, generalized Hilbert-Kunz multiplicities can be expressed as linear combinations of classical Hilbert-Kunz multiplicities.
We provide a new short proof for the Birman--Solomyak theorem for Hilbert--Schmidt operators and give an application to a Schr\"odinger--Poisson system.
The action of the Bernstein operators on Schur functions was given in terms of codes in [CG] and extended to the analog in Schur Q-functions in [HJS]. We define a new combinatorial model of extended codes and show that both of these results…
We study the orthogonality of the generalized eigenspaces of an Ornstein--Uhlenbeck operator $\mathcal L$ in $\mathbb{R}^N$, with drift given by a real matrix $B$ whose eigenvalues have negative real parts. If $B$ has only one eigenvalue,…
The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…
In this note we extend two characterizations of admissible operators with respect to $\mathrm{L}^p$ to more general Orlicz spaces. The equivalent conditions are given by the property that an associated operator generates a strongly…
We extend to manifolds endowed with a general geometric structure, the classical notions of gradient as well as Laplace operator, and provide some of their natural properties.
In this article we prove L^p estimates for a general maximal operator, which extend both the classical Coifman-Meyer and Carleson-Hunt theorems in harmonic analysis
We show that in a quite general framework, the parameterized optimization problem can be so perturbed as to be generically well-posed. As an application, we provide a contribution to Stechkin theory.
The Schur-Horn theorem is a classical result in matrix analysis which characterizes the existence of positive semidefinite matrices with a given diagonal and spectrum. In recent years, this theorem has been used to characterize the…
It is proved recently by Benamara-Nikolski that a contraction having finite defects and spectrum not filling in the closed unit disc, is similar to a normal operator if and only if it has the so-called linear resolvent growth property. We…
The Fefferman-Stein type inequality for strong maximal operator is verified with compositions of some maximal operators in the heigher dimensions. An elementary proof of the endpoint estimate for the strong maximal operator is also given.
In this paper we show that the operator introduced by A. A. Tsvetkov enjoys all the needed properties of a Q-operator. It is shown that the Q-operator of the XXX spin chain with generic values of spin turns into Tsvetkov's operator in the…
We develop a fractional extension of the classical binomial distribution and the associated Bernstein operator, formulated within the framework of the generalized binomial theorem (Hara and Hino [Bull.\ London Math.\ Soc. \textbf{42}…
We obtain some new inequalities of Chebyshev Type.
This paper proves a genericity conjecture by Goldstein, Schlag, and Voda[Invent. Math.\textbf{217}(2019)] for multi-frequency quasiperiodic Schr\"{o}dinger operators. Specifically, we show that for almost all coefficients of real…
Quasidiagonal operators on a Hilbert space are a large and important class (containing all self-adjoint operators for instance). They are also perfectly suited for study via the finite section method (a particular Galerkin method). Indeed,…
The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Our approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine…
In this paper, we characterize complementable operators and provide more precise expressions for the Schur complement of these operators using a single Douglas solution. We demonstrate the existence of subspaces where the given operator is…
The Grunsky operator arises from univalence and plays a crucial role in geometric function theory. This operator also implies quasiconformal extendibility and has an intrinsic connection with Teichmuller space theory and its interactions…