相关论文: Useful Bases for Problems in Nuclear and Particle …

Special functions have been used widely in many problems of applied sciences. However, there are considerable numbers of problems in which exact solutions could not be achieved because of undefined sums or integrals involving special…

This paper deals with some special integral transforms of Bargmann-Fock type in the setting of quaternionic valued slice hyperholomorphic and Cauchy-Fueter regular functions. The construction is based on the well-known Fueter mapping…

Trigonometric formulas are derived for certain families of associated Legendre functions of fractional degree and order, for use in approximation theory. These functions are algebraic, and when viewed as Gauss hypergeometric functions,…

Integral transforms arising from the separable solutions to the Helmholtz differential equation are presented. Pairs of these integral transforms are related via Plancherel theorem and, ultimately, any of these integral transforms may be…

We address the problem of constructing approximations based on orthogonal polynomials that preserve an arbitrary set of moments of a given function without loosing the spectral convergence property. To this aim, we compute the constrained…

A new type of basis functions is proposed to describe a two-electron continuum which arises as a final state in electron-impact ionization and double photoionization of atomic systems. We name these functions, which are calculated in terms…

The performance of basis sets made of numerical atomic orbitals is explored in density-functional calculations of solids and molecules. With the aim of optimizing basis quality while maintaining strict localization of the orbitals, as…

We calculate the least upper bounds of pointwise and uniform approximations for classes of $2\pi$-periodic functions expressible as convolutions of an arbitrary square summable kernel with functions, which belong to the unit ball of the…

Deformed correlated Gaussian basis functions are introduced and their matrix elements are calculated. These basis functions can be used to solve problems with nonspherical potentials. One example of such potential is the dipole…

Special bases of orthogonal polynomials are defined, that are suited to expansions of density and potential perturbations under strict particle number conservation. Particle-hole expansions of the density response to an arbitrary…

Using the quadratic transformation and the generating function method we Perform the Fourier transformation of the wave function of coordinates of hydrogen atom and we find the analytic expression of the wave function in momentum space. We…

We study a class of weight functions on $[-1,1]$, which are special cases of the general weights studied by Bernstein and Szeg\"o, as well as their extentions to the interval $[-a,1]$ for a continuous parameter $a>0$. These weights are…

The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order…

Adapting the recently developed randomized dyadic structures, we introduce the notion of spline function in geometrically doubling quasi-metric spaces. Such functions have interpolation and reproducing properties as the linear splines in…

A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…

Canonical quantization of electromagnetic field is traditionally done using plane waves. It is possible to formulate the quantization using other complete set of basis functions. Wavelets are a special kind of functions which are localized…

The two-nucleon spectral function in nuclear matter is studied using Correlated Basis Function perturbation theory, including central and tensor correlations produceded by a realistic hamiltonian. The factorization property of the…

We use the classical Fourier analysis to introduce analytic families of weighted differential operators on the unit sphere. These operators are polynomial functions of the usual Beltrami-Laplace operator. New inversion formulas are obtained…

The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schr\"odinger equation and account for relativistic and QED effects by perturbation…

In this work we present an explicit representation of the orthonormal Bernstein polynomials and demonstrate that they can be generated from a linear combination of non-orthonormal Bernstein polynomials. In addition, we report a set of $n$…