Related papers: A constrained optimization problem for the Fourier…
This paper proposes a closed-form optimal estimator based on the theory of estimating functions for a class of linear ARCH models. The estimating function (EF) estimator has the advantage over the widely used maximum likelihood (ML) and…
We continue our study begun in "On the integrality of the Taylor coefficients of mirror maps" (arXiv:0907.2577) of the fine integrality properties of the Taylor coefficients of the series ${\bf q}(z)=z\exp({\bf G}(z)/{\bf F}(z))$, where…
We estimate the covariance in counts of almost-primes in $\mathbb{F}_q[T]$, weighted by higher-order von Mangoldt functions. The answer takes a pleasant algebraic form. This generalizes recent work of Keating and Rudnick that estimates the…
We give a simple necessary and sufficient condition for maximal operators associated with radial Fourier multipliers to be bounded on $L^p_{rad}$ and $L^p$ for certain $p$ greater than $2$. The range of exponents obtained for the…
We derive an extremal equation for optimal completely-positive map which most closely approximates a given transformation between pure quantum states. Moreover, we also obtain an upper bound on the maximal mean fidelity that can be attained…
Entropy numbers are an important tool for quantifying the compactness of operators. Besides establishing new upper bounds on the entropy numbers of diagonal operators $D_\sigma$ from $\ell_p$ to $\ell_q$, where $p\not=q$, we investigate the…
In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…
The signs of Fourier coefficients of certain eta quotients are determined by dissecting expansions for theta functions and by applying a general dissection formula for certain classes of quintuple products. A characterization is given for…
In this paper, we provide explicit upper and lower bounds for the argument of the Riemann zeta-function and its antiderivatives in the critical strip under the assumption of the Riemann hypothesis. This extends the previously known bounds…
We prove essentially optimal $L^p(\mathbb{R})$-estimates for variational variants of the maximal Fourier multiplier operators considered by Bourgain in his work on pointwise convergence of polynomial ergodic averages. As a corollary of our…
We control a broad class of singular (or "rough") Fourier multipliers by geometrically-defined maximal operators via general weighted $L^2(\mathbb{R})$ norm inequalities. The multipliers involved are related to those of Coifman--Rubio de…
We determine the order of magnitude of $\mathbb{E}|\sum_{n \leq x} f(n)|^{2q}$ up to factors of size $e^{O(q^2)}$, where $f(n)$ is a Steinhaus or Rademacher random multiplicative function, for all real $1 \leq q \leq \frac{c\log x}{\log\log…
Weighted Poincar\'e-type and related inequalities provide upper bounds of the variance of functions. Their application in sensitivity analysis allows for quickly identifying the active inputs. Although the efficiency in prioritizing inputs…
In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a…
Let $\mathbb F_q$ be the finite field with $q$ elements, $f, g\in \mathbb F_q[x]$ be polynomials of degree at least one. This paper deals with the asymptotic growth of certain arithmetic functions associated to the factorization of the…
In this paper we prove several weighted estimates for bilinear fractional integral operators and their commutators with BMO functions. We also prove maximal function control theorem for these operators, that is, we prove the weighted $L^p$…
This article presents a discussion of optimization problems where the objective function f(x) has parameters that are constrained by some scaling, so that q(x) = constant, where this function q() involves a sum of the parameters, their…
Multivariate quasi-projection operators $Q_j(f,\varphi, \widetilde{\varphi})$, associated with a function $\varphi$ and a distribution/function $\widetilde{\varphi}$, are considered. The function $\varphi$ is supposed to satisfy the…
We consider the problem of maximizing a monotone submodular function under a knapsack constraint. We show that, for any fixed $\epsilon > 0$, there exists a polynomial-time algorithm with an approximation ratio $1-c/e-\epsilon$, where $c…
This manuscript includes some classical results we select apart from the new results we've found on the Analysis of Boolean Functions and Fourier-Entropy-Influence conjecture. We try to ensure the self-completeness of this work so that…