Related papers: Spectral function for $^4$He using the Chebyshev e…
Spectral tetris is a fexible and elementary method to construct unit norm frames with a given frame operator, having all of its eigenvalues greater than or equal to two. One important application of spectral tetris is the construction of…
We establish the asymptotic validity of frequency-domain inference for stationary multivariate Hawkes processes under mild conditions, bridging the gap between theory and application. By developing upper-bounds on the reduced cumulant…
The spectral function of the closed-shell Neon atom is computed by expanding the electron self-energy through a set of Faddeev equations. This method describes the coupling of single-particle degrees of freedom with correlated two-electron,…
Theoretical calculations of one- and two-hole spectral functions for the O16 nucleus are still failing to describe some of the important features observed experimentally. Of critical importance for the solution of these issues is to obtain…
We develop a sparse spectral method for a class of fractional differential equations, posed on $\mathbb{R}$, in one dimension. These equations can include sqrt-Laplacian, Hilbert, derivative and identity terms. The numerical method utilizes…
For Hill's equation on [0,infinity) we prove new characterizations of the spectral function rho(lambda) and the spectral density function f(lambda) based on analysis involving a companion system of first order differential equations in…
An analytical approach to the one-dimensional spinless Holstein model is proposed, which is valid at finite charge-carrier concentrations. Spectral functions of charge carriers are computed on the basis of self-energy calculations. A…
The Haar functional on the quantum $SU(2)$ group is the analogue of invariant integration on the group $SU(2)$. If restricted to a subalgebra generated by a self-adjoint element the Haar functional can be expressed as an integral with a…
A common optical potential for $^4$He+$^{12}$C at intermediate bombarding energies, which is essential in analyzing exotic nuclei with $^4$He clusters, was obtained based on the S\~{a}o Paulo potential (SPP). Among systematic optical…
We propose a novel mathematical approach for the calculation of near-zero energy states by solving potentials which are isospectral with the original one. For any potential, families of strictly isospectral potentials (with very different…
In 2016, the spectral theory on the $S$-spectrum was used to establish the $H^\infty$-functional calculus for quaternionic or Clifford operators. This calculus applies for example to sectorial or bisectorial right linear operators $T$ and…
The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral analysis in a translation invariant closed linear subspace of additive/multiadditive functions containing the…
This paper leverages the use of \emph{Gram iteration} an efficient, deterministic, and differentiable method for computing spectral norm with an upper bound guarantee. Designed for circular convolutional layers, we generalize the use of the…
Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…
Reconstructing spectral functions from propagator data is difficult as solving the analytic continuation problem or applying an inverse integral transformation are ill-conditioned problems. Recent work has proposed using neural networks to…
Many ground state studies of $^4$He using a shadow wave function with an inverse fifth power McMillan particle-particle correlation function have yielded radial distribution functions with misplaced peaks. It has been conjectured that this…
The structure of a cotangent bundle is investigated for quantum linear groups GLq(n) and SLq(n). Using a q-version of the Cayley-Hamilton theorem we construct an extension of the algebra of differential operators on SLq(n) (otherwise called…
A nuclear-elastic $^9$Be+$^4$He reaction is investigated. A tangential literature overview of the proximity potential is presented, necessitated by an approximate method for calculating $l\text{-values}$. The model is surveyed intensively,…
The new representation formula for the spectral shift function due to F.Gesztesy and K.A.Makarov is considered. This formula is extended to the case of relatively trace class perturbations.
We extend and deepen the theory of functional calculus for semigroup generators, based on the algebra $\mathcal B$ of analytic Besov functions, which we initiated in a previous paper. In particular, we show that our construction of the…