Related papers: Sharp $A_2$ estimates of Haar shifts via Bellman f…
In quantum mechanics, the wave function of fermion systems such as many-body electron systems are anti-symmetric (AS) and continuous, and it is crucial yet challenging to find an ansatz to represent them. This paper addresses this challenge…
The Heckman-Opdam hypergeometric functions of type BC extend classical Jacobi functions in one variable and include the spherical functions of non-compact Grassmann manifolds over the real, complex or quaternionic numbers. There are various…
Shifted variants of (dyadic) Hardy-Littlewood maximal function and Stein's square function have played a significant role in the study of many important operators such as Calderon commutators, (bilinear) Hilbert transforms, multilinear…
A fermionic representation is given for all the quantities entering in the generating function approach to weighted Hurwitz numbers and topological recursion. This includes: KP and 2D Toda $\tau$-functions of hypergeometric type, which…
We provide a description for the Bellman function related to the Carleson Imbedding theorem, first mentioned in [4], with the use of the Hardy operator.
For a class of sparse operators including majorants of singular integral, square function, and fractional integral operators in a uniform manner, we prove off-diagonal two-weight estimates of mixed type in the two-weight and…
We study a problem of estimation of smooth functionals of parameter $\theta $ of Gaussian shift model $$ X=\theta +\xi,\ \theta \in E, $$ where $E$ is a separable Banach space and $X$ is an observation of unknown vector $\theta$ in Gaussian…
A fast and accurate algorithm for the computation of Gauss-Hermite and generalized Gauss-Hermite quadrature nodes and weights is presented. The algorithm is based on Newton's method with carefully selected initial guesses for the nodes and…
Consider $d$ disjoint closed subintervals of the unit interval and consider an orientation preserving expanding map which maps each of these subintervals to the whole unit interval. The set of points where all iterates of this expanding map…
This paper aims to evaluate the Piterbarg-Berman function given by $$\mathcal{P\!B}_\alpha^h(x, E) = \int_\mathbb{R}e^z\mathbb{P} \left\{{\int_E \mathbb{I}\left(\sqrt2B_\alpha(t) - |t|^\alpha - h(t) - z>0 \right) {\text{d}} t > x} \right\}…
A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a…
It has been known for over 70 years that there is an asymptotic transition of Charlier polynomials to Hermite polynomials. This transition, which is still presented in its classical form in modern reference works, is valid if and only if a…
We develop new solvability methods for divergence form second order, real and complex, elliptic systems above Lipschitz graphs, with $L_2$ boundary data. The coefficients $A$ may depend on all variables, but are assumed to be close to…
A weighted Hilbert space $F^2_{\varphi}$ of entire functions of $n$ variables is considered in the paper. The weight function $\varphi$ is a convex function on ${\mathbb C}^n$ depending on modules of variables and growing at infinity faster…
The sharp constants in the classical John--Nirenberg inequality are found by using Bellman function approach.
It is known that adaptive Fourier decomposition (AFD) offers efficient rational approxima- tions to functions in the classical Hardy H2 spaces with significant applications. This study aims at rational approximation in Bergman, and more…
We establish endoscopic and stable trace formulas whose discrete spectral terms are weighted by automorphic $L$-functions, by the use of basic functions that are incorporated into the global spectral and geometric coefficients. This is a…
In this paper we present a brief description of a ladder operator formalism applied to orthogonal polynomials with discontinuous weights. The two coefficient functions, A_n(z) and B_n(z), appearing in the ladder operators satisfy the two…
We present an $L^2$-extension theorem with an estimate depending on the weight functions for domains in $\mathbb{C}$. When the Hartogs domain defined by the weight function is strictly pseudoconvex, this estimate is strictly sharper than…
The purpose of this note is to show that the di-bar-estimate which is needed in the Ohsawa-Takegoshi Extension Theorem [6] is a direct consequence of the Hormander-Kohn-Morrey weigthed inequality. In this inequality, the Donnelly-Fefferman…