Related papers: Discontinuity of the Lempert function of the spect…
We find all matrices $A$ from the spectral unit ball $\Omega_n$ such that the Lempert function $l_{\Omega_n}(A,\cdot)$ is continuous.
Some results on the discontinuity properties of the Lempert function and the Kobayashi pseudometric in the spectral ball are given.
Under certain general conditions, an explicit formula to compute the greatest delta-epsilon function of a continuous function is given. From this formula, a new way to analyze the uniform continuity of a continuous function is given.…
The lower spectral radius of a set of $d \times d$ matrices is defined to be the minimum possible exponential growth rate of long products of matrices drawn from that set. When considered as a function of a finite set of matrices of fixed…
This paper investigates continuity properties of value functions and solutions for parametric optimization problems. These problems are important in operations research, control, and economics because optimality equations are their…
The Green function of the spectral ball is constant over the isospectral varieties, is never less than the pullback of its counterpart on the symmetrized polydisk, and is equal to it in the generic case where the pole is a cyclic…
We give some sufficient conditions for preserving of the second term in the spectral asymptotics of a compact operator under the perturbation of the metrics in the Hilbert space.
We prove the the multipole Lempert function is monotone under inclusion of pole sets.
Given a domain $\Omega \subset \mathbb C$, the Lempert function is a functional on the space $Hol (\D,\Omega)$ of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. We generalize its definition to the case…
Necessary and sufficient conditions for Lipschitzness of the Lempert and Green functions are found in terms of their boundary behaviors.
In this paper we consider properties of medians as they pertain to the continuity and vanishing oscillation of a function. Our approach is based on the observation that medians are related to local sharp maximal functions restricted to a…
We characterize the continuity of prototypical functionals acting on finite Caccioppoli partitions. In the spirit of the classical Reshetnyak continuity theorem for measures that can be used to prove continuity of surface-type functionals…
The spectral diameter of a symplectic ball is shown to be equal to its capacity; this result upgrades the known bound by a factor of two and yields a simple formula for the spectral diameter of a symplectic ellipsoid. We also study the…
We give the definition of uniform symmetric continuity for functions defined on a nonempty subset of the real line. Then we investigate the properties of uniformly symmetrically continuous functions and compare them with those of…
We consider averages $\kappa$ of spectral measures of rank one perturbations with respect to a $\sigma$-finite measure $\nu$. It is examined how various degrees of continuity of $\nu$ with respect to $\alpha$-dimensional Hausdorff measures…
In this paper we extend our findings in [3] and answer further questions regarding continuity and discontinuity of seminorms on infinite-dimensional vector spaces.
In this paper we study a continuity of the "values" of modular functions at the real quadratic numbers which are defined in terms of their cycle integrals along the associated closed geodesics. Our main theorem reveals a more finer…
We establish spectral rigidity for spherically symmetric manifolds with boundary and interior interfaces determined by discontinuities in the metric under certain conditions. Rather than a single metric, we allow two distinct metrics in…
We discuss transformations on matrices that preserve the effective spectrum and/or the effective spectral radius.
This paper provides a mathematical approach to study metasurfaces in non flat geometries. Analytical conditions between the curvature of the surface and the set of refracted directions are introduced to guarantee the existence of phase…