» Matrix Extreme Points and Free extreme points of Free spectrahedra. (arXiv:2212.00748v1 [math.FA])
02/12/22 11:40 from math.FA updates on arXiv.org
A spectrahedron is a convex set defined by a linear matrix inequality, i.e., the set of all $x \in \mathbb{R}^g$ such that \[ L_A(x) = I + A_1 x_1 + A_2 x_2 + \dots + A_g x_g \succeq 0 \] for some symmetric matrices $A_1,\ldots,A_g$. Thi...

» Admissible function spaces for weighted Sobolev inequalities. (arXiv:2012.04622v3 [math.AP] UPDATED)
02/12/22 11:40 from math.FA updates on arXiv.org
Let $k,N \in \mathbb{N}$ with $1\le k\le N$ and let $\Omega=\Omega_1 \times \Omega_2$ be an open set in $\mathbb{R}^k \times \mathbb{R}^{N-k}$. For $p\in (1,\infty)$ and $q \in (0,\infty),$ we consider the following Hardy-Sobolev type in...

» Characterization of SRB Measures for Random Dynamical Systems on Banach space. (arXiv:2210.08967v3 [math.DS] UPDATED)
02/12/22 11:40 from math.FA updates on arXiv.org
This paper considers $C^2$ random dynamical systems on a Banach space, and proves that under some mild conditions, SRB measures are characterized by invariant measures satisfying the Pesin entropy formula, in which entropy is equal to th...

» A Survey on Invariant Spaces of Holomorphic Functions on Symmetric Domains. (arXiv:2211.06055v3 [math.CV] UPDATED)
02/12/22 11:40 from math.FA updates on arXiv.org
We present some old and new results on a class of invariant spaces of holomorphic functions on symmetric domains, both in their circular bounded realizations and in their unbounded realizations as Siegel domains of type II. These spaces ...

» Invariant Spaces of Holomorphic Functions on Symmetric Siegel domains. (arXiv:2211.06058v3 [math.CV] UPDATED)
02/12/22 11:40 from math.FA updates on arXiv.org
In this paper we consider a symmetric Siegel domain $D$ and some natural representations of the M\"obius group $G$ of its biholomorphisms and of the group $\mathrm{Aff}$ of its affine biholomorphisms. We provide a complete classification...

» Abstract Model of Continuous-Time Quantum Walk Based on Bernoulli Functionals and Perfect State Transfer. (arXiv:2212.00020v1 [quant-ph])
02/12/22 11:40 from math.FA updates on arXiv.org
In this paper, we present an abstract model of continuous-time quantum walk (CTQW) based on Bernoulli functionals and show that the model has perfect state transfer (PST), among others. Let $\mathfrak{h}$ be the space of square integrabl...

» The spectral form of the functional model for maximally dissipative operators: A Lagrange identity approach. (arXiv:2212.00708v1 [math.SP])
02/12/22 11:40 from math.SP updates on arXiv.org
The spectral and scattering properties of non-selfadjoint problems pose a mathematical challenge. Apart from exceptional cases, the well-developed methods used to examine the spectrum of selfadjoint problems are not applicable. One of th...

» Fourier Series in Fractional Dimensional Space. (arXiv:2212.00049v1 [math.GM])
02/12/22 11:40 from math.FA updates on arXiv.org
In this paper, a Fourier series in fractional dimensional space is introduced for an arbitrarily periodic function $f(t;\alpha)$. We call it fractional Fourier series of the order $\alpha$. Extending the basis functions of the linear spa...