Related papers: $\mathcal I^{\mathcal K}$-Cauchy functions
Holomorphic fields play an important role in 2d conformal field theory. We generalize them to d>2 by introducing the notion of Cauchy conformal fields, which satisfy a first order differential equation such that they are determined…
We construct a sequence that converges to a solution of the Cauchy problem for a singularly perturbed linear inhomogeneous differential equation of an arbitrary order. This sequence is also an asymptotic sequence in the following sense: the…
The interrelation between analytic functions and real-valued functions is formulated in the work. It is shown such an interrelation realizes nonlinear representations for real-valued functions that allows to develop new methods of…
This paper conglomerates our findings on the space $C(X)$ of all real valued continuous functions, under different generalizations of the topology of uniform convergence and the $m$-topology. The paper begins with answering all the…
The isometric universality of the spaces $C(K)$ for $K$ a non scattered Hausdorff compact does not take into account the ``quality'' of the representation. Indeed, the existence of an isometric copy of a separable Banach space $X$ into…
Parabolic integro-differential non degenerate Cauchy problem is considered in the scale of H\"older spaces of functions whose regularity is defined by a radially O-regularly varying L\'evy measure. Existence and uniqueness and the estimates…
In this paper, we will define $\mathcal{I}^{*}$-sequential topology on a topological space $(X,\tau)$ where $\mathcal{I}$ is an ideal of the subset of natural numbers $\mathbb{N}$. Besides the basic properties of the…
The Mat\'ern and the Generalized Cauchy families of covariance functions have a prominent role in spatial statistics as well as in a wealth of statistical applications. The Mat\'ern family is crucial to index mean-square differentiability…
If $\mu$ is a finite complex measure in the complex plane $\C$ we denote by $C^\mu$ its Cauchy integral defined in the sense of principal value. The measure $\mu$ is called reflectionless if it is continuous (has no atoms) and $C^\mu=0$ at…
In this paper we study left and right n-regular functions that originally were introduced in [FL4]. When n=1, these functions are the usual quaternionic left and right regular functions. We show that n-regular functions satisfy most of the…
In the paper, the authors analytically generalize the Catalan numbers in combinatorial number theory, establish an integral representation of the analytic generalization of the Catalan numbers by virtue of Cauchy's integral formula in the…
In this paper we introduce I^K-convergence which is a common generalization of the I^K-convergence of sequences, double sequences and nets. We show that many results that were shown before for these special cases are true for the…
We prove that the $f$-divergences between univariate Cauchy distributions are all symmetric, and can be expressed as strictly increasing scalar functions of the symmetric chi-squared divergence. We report the corresponding scalar functions…
We generalize the notion of K\"ulshammer ideals to the setting of a graded category. This allows us to define and study some properties of K\"ulshammer type ideals in the graded center of a triangulated category and in the Hochschild…
In this paper we give three functors $\mathfrak{P}$, $[\cdot]_K$ and $\mathfrak{F}$ on the category of C$^\ast$-algebras. The functor $\mathfrak{P}$ assigns to each C$^\ast$-algebra $\mathcal{A}$ a pre-C$^\ast$-algebra…
We develop foundational tools for classifying the extreme valid functions for the k-dimensional infinite group problem. In particular, (1) we present the general regular solution to Cauchy's additive functional equation on bounded convex…
An ideal on a set $X$ is a collection of subsets of $X$ closed under the operations of taking finite unions and subsets of its elements. Ideals are a very useful notion in topology and set theory and have been studied for a long time. We…
It is consistent with constructive set theory (without Countable Choice, clearly) that the Cauchy reals (equivalence classes of Cauchy sequences of rationals) are not Cauchy complete. Related results are also shown, such as that a Cauchy…
In this paper, we introduce the notion of a Klyachko diagram for a monomial ideal $I$ in a certain multi-graded polynomial ring, namely the Cox ring $R$ of a smooth complete toric variety, with irrelevant maximal ideal $B$. We present…
It is shown that every set I(m) of Banach lattices of measurable functions defined on a measure space (Q,S,m), equipped with a some natural ordering became a modular lattice, which is Dedekind complete provided m is a probability measure.…