相关论文: Oscillatory integral operators with low-order dege…

In the paper we prove several inequalities involving two isotonic linear functionals. We consider inequalities for functions with variable bounds, for Lipschitz and H\" older type functions etc. These results give us an elegant method for…

We prove a variable coefficient version of the square function estimate of Guth--Wang--Zhang. By a classical argument of Mockenhaupt--Seeger--Sogge, it implies the full range of sharp local smoothing estimates for $2+1$ dimensional Fourier…

A class of cross-shaped difference operators on a two dimensional lattice is introduced. The main feature of the operators in this class is that their formal eigenvectors consist of multiple orthogonal polynomials. In other words, this…

Using the shift-operator technique, a compact formula for the Fourier transform of a product of two Slater-type orbitals located on different atomic centers is derived. The result is valid for arbitrary quantum numbers and was found to be…

The main aim of this article is to establish an $L_p$-theory for elliptic operators on manifolds with singularities. The particular class of differential operators discussed herein may exhibit degenerate or singular behavior near the…

In this paper we study sharp estimates for the Schr\"odinger operator via the framework of orthogonal polynomials. We use spherical harmonics and Gegenbauer polynomials to prove a new weighted inequality for the Schr\"odinger equation that…

Pseudo-differential and Fourier series operators on the n-torus are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal symbols are investigated and the correspondence…

A scheme is proposed which allows to obtain special $q$-oscillator models whose characteristic feature consists in possessing two differing pairs of degenerate energy levels. The method uses the model of two-parameter deformed…

In this paper, a family of radial deformations of the realization of the Lie superalgebra osp(1|2) in the theory of Dunkl operators is obtained. This leads to a Dirac operator depending on 3 parameters. Several function theoretical aspects…

In this paper, a finite set of biorthogonal polynomials in two variables is produced using Konhauser polynomials. Some properties containing operational and integral representation, Laplace transform, fractional calculus operators of this…

This article gives a fundamental discussion on variable coefficients, self-adjoint, formally partially hypoelliptic differential operators. A generalization of the results to pseudo differential operators, is given in a following article in…

The definition for the Slater-type orbitals is generalized. Transformation between an orthonormal basis function and the Slater-type orbital with non-integer principal quantum numbers is investigated. Analytical expressions for the linear…

We show that the Hardy spaces for Fourier integral operators form natural spaces of initial data when applying $\ell^{p}$-decoupling inequalities to local smoothing for the wave equation. This yields new local smoothing estimates which, in…

In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…

In this paper, we first prove some local estimates for bilinear operators (closely related to the bilinear Hilbert transform and similar singular operators) with truncated symbol. Such estimates, in accordance with the Heisenberg…

This paper addresses particular eigenvalue problems within the context of two quaternionic function theories. More precisely, we study two concrete classes of quaternionic eigenvalue problems, the first one for the slice derivative operator…

Basic questions concerning nonsingular multilinear operators with oscillatory factors are posed and partially answered. Lebesgue space norm inequalities are established for multilinear integral operators of Calderon-Zygmund type which…

Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being obtained from the corresponding classical integrals by a symmetrization procedure. For each quantum…

Spectrum of a certain class of first order conformally invariant operators on the sphere is explicitly computed. The class contains the (elliptic verions of) Rarita-Schwinger operator and its higher spin analogues.

Approximate $p$-point Leibniz derivation formulas as well as interpolatory Simpson quadrature sums adapted to oscillatory functions are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the…