Related papers: Analytic Function Theory for Operator-Valued Free …

The asymptotic analysis of covariance parameter estimation of Gaussian processes has been subject to intensive investigation. However, this asymptotic analysis is very scarce for non-Gaussian processes. In this paper, we study a class of…

We study asymptotic expansions in free probability. In a class of classical limit theorems Edgeworth expansion can be obtained via a general approach using sequences of "influence" functions of individual random elements described by…

This paper defines, on the Galilean space-time, the group of asymptotically Euclidean transformations (AET), which are equivalent to Euclidean transformations at space-time infinity, and proposes a formulation of nonrelativistic quantum…

Let $\mathcal{N}$ be a non-Archimedean ordered field extension of the real numbers that is real closed and Cauchy complete in the topology induced by the order, and whose Hahn group is Archimedean. In this paper, we first review the…

We introduce a new type of shift dynamics as an extended model of symbolic dynamics, and investigate the characteristics of shift spaces from the viewpoints of both dynamics and computation. This shift dynamics is called a functional shift…

We discuss the classes $\fC$, $\fM$, and $\fS$ of analytic functions that can be realized as the Liv\v{s}ic characteristic functions of a symmetric densely defined operator $\dot A$ with deficiency indices $(1,1)$, the Weyl-Titchmarsh…

We develop a general framework to investigate fluctuations of non-commuting observables. To this end, we consider the Keldysh quasi-probability distribution (KQPD). This distribution provides a measurement-independent description of the…

In classical function theory, a function is holomorphic if and only if it is complex analytic. For higher dimensional spaces it is natural to work in the context of Clifford algebras. The structures of these algebras depend on the parity of…

We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…

Denoting by $\mathbb{M}$ the complexification of the quaternionic algebra $\mathbb{H}$, we characterize the family of those $\mathbb{M}$-valued functions, defined on subsets of $\H$, whose values are actually quaternions, using an intrinsic…

This is (raw) lecture notes of the course read on 6th European intensive course on Complex Analysis (Coimbra, Portugal) in 2000. Our purpose is to describe a general framework for generalizations of the complex analysis. As a consequence a…

We derive asymptotic estimates at infinity for positive harmonic functions in a large class of non-smooth unbounded domains. These include domains whose sections, after rescaling, resemble a Lipschitz cylinder or a Lipschitz cone, e.g.,…

For a monic polynomial $Q_n$ of degree $n$, let $Q_{n, k}$ be its $k$-th derivative normalized to be monic. Under the only assumption that the sequence $\{Q_n\}$ has a weak* limiting zero distribution (an empirical distribution of zeros)…

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…

We present a simple result that allows us to evaluate the asymptotic order of the remainder of a partial asymptotic expansion of the quantile function $h(u)$ as $u\to 0^+$ or $1^-$. This is focussed on important univariate distributions…

We introduce an experimental test for ruling out classical explanations for the statistics obtained when measuring arbitrary observables at arbitrary times using individual detectors. This test requires some trust in the measurements,…

In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its…

Many observables in quantum field theories are involved non-analytic functions of the parameters of the theory. However, it is expected that they are not arbitrarily wild, but rather have only a finite amount of geometric complexity. This…

Recently, it was realized that anomalies can be completely classified by topological orders, symmetry protected topological (SPT) orders, and symmetry enriched topological orders in one higher dimension. The anomalies that people used to…

In this paper we study the asymptotic zero distribution of eigenpolynomials for degenerate exactly-solvable operators. We present an explicit conjecture and partial results on the growth of the largest modulus of the roots of the unique and…