Related papers: Algorithms for estimating spectral density functio…
In this paper we discuss spectral properties of operators associated with the least-squares finite element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the…
We prove an estimate for spherical functions $\varphi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian…
We consider the problem of estimating the fractional order of a L\'{e}vy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a…
Given $\rho\in(0, 1/3]$, let $\mu$ be the Cantor measure satisfying $\mu=\frac{1}{2}\mu f_0^{-1}+\frac{1}{2}\mu f_1^{-1}$, where $f_i(x)=\rho x+i(1-\rho)$ for $i=0, 1$. The support of $\mu$ is a Cantor set $C$ generated by the iterated…
We consider an elliptic self-adjoint first order pseudodifferential operator acting on columns of complex-valued half-densities over a connected compact manifold without boundary. The eigenvalues of the principal symbol are assumed to be…
In this paper, spectral analysis of fractional Sturm Liouville problem defined on (0,1], having the singularity of type at zero and research the fundamental properties of the eigenfunctions and eigenvalues for the operator. We show that the…
We obtain a representation formula for the derivative of the spectral shift function $\xi(\lambda; B, \epsilon)$ related to the operators $H_0(B,\epsilon) = (D_x - By)^2 + D_y^2 + \epsilon x$ and $H(B, \epsilon) = H_0(B, \epsilon) + V(x,y),…
Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a…
Originally motivated by a stability problem in Fluid Mechanics, we study the spectral and pseudospectral properties of the differential operator $H_\epsilon = -\partial_x^2 + x^2 + i\epsilon^{-1}f(x)$ on $L^2(R)$, where $f$ is a real-valued…
Range-separated hybrid functionals (RSH) with ``ionization energy'' and/or ``optimal tuning'' of the screening parameter have proven to be among the most practical and accurate approaches for describing excited-state properties across a…
This is a follow-up of our recently proposed work on pseudopotential calculation (Ref. [21]) of atoms and molecules within DFT framework, using cartesian coordinate grid. Detailed results are presented to demonstrate the usefulness,…
The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the…
We test the applicability of density functional theory (DFT) to spectral perturbations taking an example of a Cs atom surrounded by superfluid helium. The atomic DFT of helium is used to obtain the distribution of helium atoms around the…
Motivated by Lazer-Leach type results, we study the existence of periodic solutions for systems of functional-differential equations at resonance with an arbitrary even-dimensional kernel and linear deviating terms involving a general delay…
In this work we study in a formal way the density dependent hadron field theory at finite temperature for nuclear matter. The thermodynamical potential and related quantities, as energy density and pressure are derived in two different…
A basic concept to calculate physical features of non-ideal plasmas, such as optical properties, is the spectral function which is linked to the self-energy. We calculate the spectral function for a non-relativistic hydrogen plasma in…
Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often…
The spectral function for an electron one-component plasma is calculated self-consistently using the GW0 approximation for the single-particle self-energy. In this way, correlation effects which go beyond the mean-field description of the…
The Lagrange spectrum $L$ is the set of finite values of the best approximation constants $k(\alpha)=\limsup_{|p|,|q|\to \infty}|q(q\alpha-p)|^{-1}$, where $\alpha\in \mathbb{R}\setminus \mathbb{Q}$. It is a classical result that the pairs…
This paper considers the problem of specifying a simple approximating density function for a given data set (x_1,...,x_n). Simplicity is measured by the number of modes but several different definitions of approximation are introduced. The…