Related papers: Generalized Functions Beyond Distributions
The aim of this paper is to exhibit a method for proving that certain analytic functions are not solutions of algebraic differential equations. The method is based on model-theoretic properties of differential fields and properties of…
In this paper we define a notion of partial APNness and find various characterizations and constructions of classes of functions satisfying this condition. We connect this notion to the known conjecture that APN functions modified at a…
In literature, it is common to find problems which require a way to encode a finite set of information into a single data; usually means are used for that. An important generalization of means are the so called Aggregation Functions, with a…
Models of computation operating over the real numbers and computing a larger class of functions compared to the class of general recursive functions invariably introduce a non-finite element of infinite information encoded in an arbitrary…
Functions whose composition with every metric is a metric are said to be metric-preserving. In this article, we investigate a variation of the concept of metric-preserving functions where metrics are replaced by ultrametrics.
Nonstandard graphs have been defined and examined in prior works. The present work does the same for nonstandard digraphs. Since digraphs have more structure than do graphs, the present discussion requires more complicated definitions and…
Multisets are sets that allow repetition of elements. As such, multisets pave the way to a number of interesting possibilities of theoretical and applied nature. In the present work, after revising the main aspects of traditional sets, we…
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…
We consider metric ultraproducts of finite groups with respect to some classes of length functions. All sofic groups embed into these ultraproducts. We study embeddings of normed groups. We also show that in some natural situations such an…
We give a new characterization of the Baire class 1 functions (defined on an ultrametric space) by proving that they are exactly the pointwise limits of sequences of full functions (which are particularly simple Lipschitz functions).…
We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…
Hypercomplex numbers are unital algebras over the real numbers. We offer a short demonstration of the practical value of hypercomplex analytic functions in the field of partial differential equations.
We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.
From the simplest point of view, transseries are a new kind of expansion for real-valued functions. But transseries constitute much more than that--they have a very rich (algebraic, combinatorial, analytic) structure. The set of transseries…
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…
Submodular Functions are a special class of set functions, which generalize several information-theoretic quantities such as entropy and mutual information [1]. Submodular functions have subgradients and subdifferentials [2] and admit…
We introduce a notion of a noncommutative function defined on a domain of $d$-tuples of bounded operators on an infinite dimensional Hilbert space. Inverse and implicit function theorems in this setting are established. When these…
The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new…
Chirped sinosoids and interferometric phase plots are functions that are not periodic, but are the composition of a smooth function and a periodic function. These functions functions factor into a pair of maps: from their domain to a…
Double $L$-functions are the generalization of Dirichlet $L$-functions to two variable functions. We investigate the order estimation of double $L$-functions, and give upper bounds which are explicit in conductor aspect.