经典分析与常微分方程

We consider a class of $n^{\text{th}}$-order linear ordinary differential equations with a large parameter $u$. Analytic solutions of these equations can be described by (divergent) formal series in descending powers of $u$. We demonstrate…

We study a specific class of Fourier integral operators characterized by symbols belonging to the multi-parameter H\"ormander class $\mathbf{S}^m(\R^{ n_1} \times \R^{ n_2} \times \cdots \times \R^{n_d} )$, where $n= n_1 + n_2 +\cdots +…

This paper explores the properties of multipliers associated with discrete analogues of fractional integrals, revealing intriguing connections with Dirichlet characters, Euler's identity, and Dedekind zeta functions of quadratic imaginary…

We derive necessary and sufficient conditions for universality limits for orthogonal polynomials on the real line and related systems. One of our results is that the Christoffel-Darboux kernel has sine kernel asymptotics at a point $\xi$,…

In the current article, we establish a distinct version of the operators defined by Berwal \emph{et al.}, which is the Kantorovich type modification of $\alpha$-Bernstein operators to approximate Lebesgue's integrable functions. We define…

We give new formulas for reconstructions from band-limited Hankel transform of integer or half-integer order. Our formulas rely on the PSWF-Radon approach to super-resolution in multidimensional Fourier analysis. This approach consists of…

This paper begins by deriving the uniform bounds for the regular Coulomb wave function $F_{\ell,\eta}$ and its derivative $F_{\ell,\eta}'$. We then examine detailed zero configurations of $F_{\ell,\eta}$ and $F_{\ell+1,\eta}$, extending…

In this paper, we establish quantitative weak type estimates for operators that are dominated by (fractional) sparse operators in bilinear sense. Specifically, we derive bounds for both the restricted weak type $L^{p,1}\rightarrow…

This paper investigates a generalized interlacing property between Bessel functions, particularly $J_\nu$ and $J_\mu$, where the difference $|\nu-\mu|$ exceeds $2$. This interlacing phenomenon is marked by a compensatory interaction with…

Given a bivariate weight function defined on the positive quadrant of $\mathbb{R}^2$, we study polynomials in two variables orthogonal with respect to varying measures obtained by special modifications of this weight function. In…

We study probability measures that minimize the Riesz energy with respect to the geodesic distance $\vartheta (x,y)$ on projective spaces $\mathbb{FP}^d$ (such energies arise from the 1959 conjecture of Fejes T\'oth about sums of non-obtuse…

We introduce a set of special functions called multiple polyexponential integrals, defined as iterated integrals of the exponential integral $\text{Ei}(z)$. These functions arise in certain perturbative expansions of the local solutions of…

The purpose of this paper is to investigate the principal spectral theory and asymptotic behavior of the spectral bound for cooperative nonlocal dispersal systems, specifically focusing on the case where partial diffusion coefficients are…

This work explores classical discrete multiple orthogonal polynomials, including Hahn, Meixner of the first and second kinds, Kravchuk, and Charlier polynomials, with an arbitrary number of weights. Explicit expressions for the recursion…

We consider Marcinkiewicz multipliers of any lacunary order defined by means of uniformly bounded variation on each lacunary Littlewood--Paley interval of some fixed order $\tau\geq 1$. We prove the optimal endpoint bounds for such…

We study the elliptic maximal functions defined by averages over ellipses and rotated ellipses which are multi-parametric variants of the circular maximal function. We prove that those maximal functions are bounded on $L^p$ for some $p\neq…

In this paper, the main aim is to demonstrate the boundedness for commutators of (fractional) maximal function and sharp maximal function in the slice spaces, where the symbols of the commutators belong to the BMO space, whereby some new…

We study the constant $\mathscr{C}_p$ defined as the smallest constant $C$ such that $|f(0)|^p \leq C\|f\|_p^p$ holds for every function $f$ in the Paley-Wiener space $PW^p$. Brevig, Chirre, Ortega-Cerd\`a, and Seip have recently shown that…

Using properties of the Fourier transform we prove that if a Hartree-Fock molecular spatial orbital is in $L_1(\mathbb{R}^3)$, then it decays to zero as its argument diverges to infinity. The proof is rigorous, elementary, and short. Our…

In this paper we study a class of Fourier integral operators, whose symbols lie in the multi-parameter H\"ormander class $S^{\vec m}( \mathbb{R}^\vn)$, where ~$\vec m=(m_1,m_2,\dots,m_d)$ is the order. We show that if in addition the phase…