Related papers: Analyticity and supershift with regular sampling
The notion of supershift generalizes that one of superoscillation and expresses the fact that the sampling of a function in an interval allows to compute the values of the function outside the interval. In a previous paper we discussed the…
Superoscillations have roots in various scientific disciplines, including optics, signal processing, radar theory, and quantum mechanics. This intriguing mathematical phenomenon permits specific functions to oscillate at a rate surpassing…
The notion of analyticity is studied in the context of hypercomplex numbers. A critical review of the problems arising from the conventional approach is given. We describe a local analyticity condition which yields the desired type of…
Arithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with respect to addition. In consequence, whenever one encounters…
Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter…
Considered are operators that leave the set of non-invertible (in the sense of Ehrenpreis) distributions stable. They simultaneously generalise the operation of convolution by a distribution with compact support and the operation of…
Analyticity results of expected pressure and invariant densities in the context of random dynamics of transcendental functions are established. These are obtained by a refinement of work by Rugh leading to a simple approach to analyticity.…
We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized…
In this paper a notion of functional "distance" in the Mellin transform setting is introduced and a general representation formula is obtained for it. Also, a determination of the distance is given in terms of Lipschitz classes and…
In the past 50 years, quantum physicists have discovered, and experimentally demonstrated, a phenomenon which they termed superoscillations. Aharonov and his collaborators showed that superoscillations naturally arise when dealing with weak…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
Recent years have witnessed the introduction and development of extremely fast rational function algorithms. Many ideas in this realm arose from polynomial-based linear-algebraic algorithms. However, polynomial approximation is occasionally…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear (abstract affine) functions. The purpose of this paper is to…
When modelling spacetime and classical physical fields, one typically assumes smoothness (infinite differentiability). But this assumption and its philosophical implications have not been sufficiently scrutinized. For example, we can appeal…
We consider a sequence of successively more restrictive definitions of abstraction for causal models, starting with a notion introduced by Rubenstein et al. (2017) called exact transformation that applies to probabilistic causal models,…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
In the framework of superanalysis we get a functions theory close to complex analysis, under a suitable condition (A) on the real superalgebras in consideration (this condition is a generalization of the classical relation 1 + i^2 = 0 in…
By comparing Schr\"odinger's cat with its classical counterpart, I show that a quantum superposition should be understood as an expectation over possible eigenstates weighted by wave-like probabilities. Upon the occurrence of a certain…