Related papers: Some constants related to numerical ranges
Mathematical diffraction theory is concerned with the analysis of the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and…
We define a new numerical range of an n\timesn complex matrix in terms of correlation matrices and develop some of its properties. We also define a related numerical range that arises from Alain Connes' famous embedding problem.
We formulate the problem of numerical analytic continuation in a way that lets us draw meaningful conclusions about properties of the spectral function based solely on the input data. Apart from ensuring consistency with the input data…
The descent set D(w) of a permutation w of 1,2,...,n is a standard and well-studied statistic. We introduce a new statistic, the connectivity set C(w), and show that it is a kind of dual object to D(w). The duality is stated in terms of the…
For a complex $n$-by-$n$ matrix $A$, the numerical range $F(A)$ is the range of the map $f_A(x) = x^*A x$ acting on the unit sphere in $\C^n$. We ask whether the multivalued inverse numerical range map $f_A^{-1}$ has a continuous…
The observables in a single-channel $2$-body scattering problem remain invariant once the amplitude is multiplied by an overall energy- and angle-dependent phase. This invariance is known as the continuum ambiguity. Also, mostly in…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
We study the dynamical equations for two-family neutrino oscillations in a medium of continuously-varying density. We can find explicit solutions to these equations in terms of series of nested integrals. These solutions can serve as a…
Statistical parametric models are proposed to explain the values of the Planck constant obtained by comparing electrical and mechanical powers and by counting atoms in Si 28 enriched crystals. They assume that uncertainty contributions --…
We study the correspondence between the linear matrix model and the interacting nonlinear string theory. Starting from the simple matrix harmonic oscillator states, we derive in a direct way scattering amplitudes of 2-dimensional strings,…
We study the gaps between consecutive singular values of random rectangular matrices. Specifically, if $M$ is an $n \times p$ random matrix with independent and identically distributed entries and $\Sigma$ is a $n \times n$ deterministic…
It has been conjectured that the mass spectrum of the O(3) non-linear sigma model with a theta term in 2 dimensions may possess an excited state, which decays when theta is lowered from pi below a critical value. Since the direct numerical…
We obtain several upper and lower bounds for the numerical radius of sectorial matrices. We also develop several numerical radius inequalities of the sum, product and commutator of sectorial matrices. The inequalities obtained here are…
We study the relation between the intrinsic and the spatial numerical ranges with the recently introduced "approximated" spatial numerical range. As main result, we show that the intrinsic numerical range always coincides with the convex…
We characterize the d x d matrices whose numerical ranges are invariant by rotations of angle 2$\pi$/d.
The first paper in this series introduced a new family of nonasymptotic matrix concentration inequalities that sharply capture the spectral properties of very general random matrices in terms of an associated noncommutative model. These…
The concept of spectrum for a class of non-linear wave equations is studied. Instead of looking for stability, the key to the spectral structure is found in the instability phenomena (bifurcations). This aspect is best seen in the…
It is well known that the arithmetic nature of Mills' prime-representing constant is uncertain: we do not know if Mills' constant is a rational or irrational number. In the case of other prime-representing constants, irrationality can be…
Coorbit spaces provide a rigorous framework for the assessment of the approximation theoretic properties of generalized wavelet systems. It is therefore useful to understand when two different wavelet systems give rise to the same scales of…
We look at invariance of a.e. boundary condition spectral behavior under perturbations, $W$, of half-line, continuum or discrete Schr\"odinger operators. We extend the results of del Rio, Simon, Stolz from compactly supported $W$'s to…