112 citations · 1.1k across the 124 of their papers we have counts for
40 papers · 1 filter
Lower and upper bounds for configurations of points on a sphere
Paolo Amore, Ricardo A. Sáenz
We present a new proof (based on spectral decomposition) of a bound originally proved by Sidelnikov~\, for the frame potentials $\sum_{ij} \left( {\bf P}_i \cdot {\bf P}_j \right)^…
Spectral sum rules for the Schrödinger equation
Paolo Amore
We study the sum rules of the form , where are the eigenvalues of the time--independent Schrödinger equation (in one or more dimensions) and is a…
On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue)
Paolo Amore
We generalize the calculation of Ref.~\cite{Amore19B} to the case of a spectrum containing a zero mode. Using a renormalization procedure, we express the sum rules in terms of suit…
On the calculation of exact sum rules of rational order for quantum billiards
Paolo Amore
We study the Helmholtz equation for a heterogeneous system in dimensions and show that it is possible to calculate exactly the sum rules of rational order using perturbation th…
Exact sum rules for heterogeneous spherical drums
Paolo Amore
We have obtained explicit integral expressions for the sums of inverse powers of the eigenvalues of the Laplacian on a unit sphere, in presence of an arbitrary variable density. Th…
On the application of the Lindstedt-Poincaré method to the Lotka-Volterra system
Paolo Amore, Francisco M. Fernández
We apply the Lindstedt-Poincaré method to the Lotka-Volterra model and discuss alternative implementations of the approach. By means of an efficient systematic algorithm we obtain…