Related papers: Cauchy transforms arising from homomorphic conditi…
In this paper, we give formulas that allow one to move between transfer function type realizations of multi-variate Schur, Herglotz and Pick functions, without adding additional singularities except perhaps poles coming from the conformal…
We show how Cauchy's Integral Formula and the ideas of Dunford's Holomorphic Functional Calculus (for unbounded operators) can be used to compute the Vacuum Characteristic Function (Quantum Fourier Transform) of quantum random variables…
We study a new hermitian one-matrix model containing a logarithmic Penner's type term and another term, which can be obtained as a limit from logarithmic terms. For small coupling, the potential has an absolute minimum at the origin, but…
We consider the Cauchy problem for doubly nonlinear degenerate parabolic equations with inhomogeneous density on noncompact Riemannian manifolds. We give a qualitative classification of the behavior of the solutions of the problem depending…
We study gradient field models on an integer lattice with non-convex interactions. These models emerge in distinct branches of physics and mathematics under various names. In particular, as zero-mass lattice (Euclidean) quantum field…
In this paper, we study free pluriharmonic functions on noncommutative balls, and their boundary behavior. The main tools used in this study are certain noncommutative transforms which are introduced in the present paper and which…
We discuss when law-invariant convex functionals "collapse to the mean". More precisely, we show that, in a large class of spaces of random variables and under mild semicontinuity assumptions, the expectation functional is, up to an affine…
This work is devoted to the analysis of the asymptotic behaviour of a parameter dependent quasilinear cooperative eigenvalue system when a parameter in front of some non-negative potentials goes to infinity. In particular we consider…
In this paper, we provide quantitative versions of results on the asymptotic behavior of nonlinear semigroups generated by an accretive operator due to O. Nevanlinna and S. Reich as well as H.-K. Xu. These results themselves rely on a…
We study Nevai's condition from the theory of orthogonal polynomials on the real line. We prove that a large class of measures with unbounded Jacobi parameters satisfies Nevai's condition locally uniformly on the support of the measure away…
A sharp, distribution free, non-asymptotic result is proved for the concentration of a random function around the mean function, when the randomization is generated by a finite sequence of independent data and the random functions satisfy…
Let $\Omega$ be a Cartan domain and $K = \sum_{\underline s}a_{\underline s}K_{\underline s}$ be a $\mathbb K$-invariant kernel on $\Omega$. In this article, we first obtain a necessary condition on $K$ to have the complete Nevanlinna-Pick…
We consider a family of conditional nonlinear expectations defined on the space of bounded random variables and indexed by the class of all the sub-sigma-algebras of a given underlying sigma-algebra. We show that if this family satisfies a…
Solutions for a class of wave equations with effective potentials are obtained by a method of a Laplace-transform. Quasinormal modes appear naturally in the solutions only in a spatially truncated form; their coefficients are uniquely…
The motivation behind this paper is threefold. Firstly, to study, characterize and realize operator concavity along with its applications to operator monotonicity of free functions on operator domains that are not assumed to be matrix…
The purpose of this article is to present a result on the existence of Cauchy temporal functions invariant by the action of a compact group of conformal transformations in arbitrary globally hyperbolic manifolds. Moreover, the previous…
The Nevanlinna transform K(z), of a measure and a real constant, plays an important role in the complex analysis and more recently in the free probability theory (boolean convolution). It is shown that its restriction k(it) (the restricted…
We prove generalizations of L\"owner's results on matrix monotone functions to several variables. We give a characterization of when a function of $d$ variables is locally monotone on $d$-tuples of commuting self-adjoint $n$-by-$n$…
We give new sufficient conditions for a compact set $E \subseteq \mathbb{C}$ to satisfy $\gamma(E)=\gamma_c(E)$, where $\gamma$ is the analytic capacity and $\gamma_c$ is the Cauchy capacity. As a consequence, we provide examples of compact…
In this paper we study the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients in some spaces of $\omega$-ultradifferentiable functions in the sense of Braun, Meise and Taylor, for…