Related papers: Galois Connections for Generalized Functions and R…
We introduce and analyse a general class of not necessarily bounded multiplicative functions, examples of which include the function $n \mapsto \delta^{\omega (n)}$, where $\delta \neq 0$ and where $\omega$ counts the number of distinct…
A generalization $\mathfrak{Gal}_{\ell}(p,q)$ of the conformal Galilei algebra $\mathfrak{g}_{\ell}(d)$ with Levi subalgebra isomorphic to $\mathfrak{sl}(2,\mathbb{R})\oplus\mathfrak{so}(p,q)$ is introduced and a virtual copy of the latter…
We study an $\ell$-adic Galois analogue of the distribution formulas for polylogarithms with special emphasis on path dependency and arithmetic behaviors. As a goal, we obtain a notion of certain universal Kummer-Heisenberg measures that…
In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…
In [S. Basu, A. Gabrielov, N. Vorobjov, Semi-monotone sets. arXiv:1004.5047v2 (2011)] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals, and having connected intersections with all…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
In this paper, we introduce a subclass of p-valent non-bazilavec functions of order. Some subordination relations and the inequality properties of p-valent functions are discussed. The results presented here generalize and improve some…
We classify all cubic function fields over any finite field, particularly developing a complete Galois theory which includes those cases when the constant field is missing certain roots of unity. In doing so, we find criteria which allow…
A variety of "pseudo-Voigt" functions, i.e. a linear combination of the Lorentz and Gauss function (occasionally augmented with a correction term), have been proposed as a closed-form approximation for the convolution of the Lorentz and…
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 $[2]$.
We study the complexity classes P and NP through a semigroup fP ("polynomial-time functions"), consisting of all polynomially balanced polynomial-time computable partial functions. Then P is not equal to NP iff fP is a non-regular…
We have shown that in some region where the Euler integral of the first kind diverges, the Euler formula defines a generalized function. The connected of this generalized function with the Dirac delta function is found.
Inspired by nonstandard analysis, we define and study internal subsets and internal functions in algebras of Colombeau generalized functions. We prove a saturation principle for internal sets and provide applications to Colombeau algebras.
This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.
Galois connections are a foundational tool for structuring abstraction in semantics and their use lies at the heart of the theory of abstract interpretation. Yet, mechanization of Galois connections remains limited to restricted modes of…
The present article is devoted to one class of generalizations of the Salem functions. To construct such functions by systems of functional equations, the generalized shift operator is used.
Galois connections are a foundational tool for structuring abstraction in semantics and their use lies at the heart of the theory of abstract interpretation. Yet, mechanization of Galois connections using proof assistants remains limited to…
We give an overview of the development of algebras of generalized functions in the sense of Colombeau and recent advances concerning diffeomorphism invariant global algebras of generalized functions and tensor fields. We furthermore provide…
Embedding Calculus, as described by Weiss, is a calculus of functors, suitable for studying contravariant functors from the poset of open subsets of a smooth manifold M, denoted O(M), to a category of topological spaces (of which the…
It is well known that over an infinite field the ring of symmetric functions in a finite number of variables is isomorphic to the one of polynomial functions on matrices that are invariants by the action of conjugation by general linear…