Related papers: A Classification of Elements of Function Space $F(…
All continuous, SL$(n)$ and translation invariant valuations on the space of convex functions on ${\mathbb R}^n$ are completely classified.
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
Regarding quaternions as normal matrices, we first characterize the $2\times 2$ matrix-valued functions, defined on subsets of quaternions, whose values are quaternions. Then we investigate the regularity of quaternionic-valued functions,…
The results presented in this paper are refinements of some results presented in a previous paper. Three such refined results are presented. The first one relaxes one of the basic hypotheses assumed in the previous paper, and thus extends…
In this paper, we study the regularity of $\mathbb{R}$-differentiable functions on open connected subsets of the scaled hypercomplex numbers $\left\{ \mathbb{H}_{t}\right\} _{t\in\mathbb{R}}$ by studying the kernels of suitable differential…
We establish an analogue of the first fundamental theorem of calculus for functions defined on the Wasserstein space of probability measures. Precisely, we show that if a function on the Wasserstein space is sufficiently regular in the…
The purpose is to formulate a Fourier transformation for the space of functionals, as an infinitesimal meaning. We extend ${\bf R}$ to $ ^{\star}(^{\ast}{\bf R})$ under the base of nonstandard methods for the construction. The domain of a…
This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In a previous paper, we introduce the notion of formal manifolds and develop the…
In the context of the correspondence between real functions on the unit circle and inner analytic functions within the open unit disk, that was presented in previous papers, we show that the constructions used to establish that…
The {\it profile} of a relational structure $R$ is the function $\phi_R$ which counts for every integer $n$ the number of its $n$-element substructures up to an isomorphism. Many counting functions are profiles. Interesting examples come…
The classical theory of free analysis generalizes the noncommutative (nc) polynomials and rational functions, easily providing such results as an nc analogue of the Jacobian conjecture. However, the classical theory misses out on important…
We formulate a set of general rules for computing $d$-dimensional four-point global conformal blocks of operators in arbitrary Lorentz representations in the context of the embedding space operator product expansion formalism…
This is an introduction to calculus, and its applications to basic questions from physics. We first discuss the theory of functions $f:\mathbb R\to\mathbb R$, with the notion of continuity, and the construction of the derivative $f'(x)$ and…
In this paper, we present explicit expressions for conforming finite element function spaces, basis functions, and degrees of freedom on the pentatope and tetrahedral prism elements. More generally, our objective is to construct finite…
We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure…
The spaces $A^s_{p,q}({\mathbb R}^n)$ with $A \in \{B,F \}$, $s\in {\mathbb R}$ and $0<p,q \le \infty$ are usually introduced in terms of Fourier--analytical decompositions. Related characterizations based on atoms and wavelets are known…
This is an exposition of the work of O. Riemenschneider about five ''circles'' of implications relating real analysis theorems each equivalent to the Dedekind completeness of the real field. These circles cover five elements of real…
We consider the space of real-valued continuously differentiable functions on a compact subset of a euclidean space. We characterize the completeness of this space and prove that the space of restrictions of continuously differentiable…
Function (linear) spaces on which an arbitrary function operates (i.e. the space is stable w.r.t. the pointwise unary operation defined by the function) were investigated, for continuous real or complex operations, by deLeeuw-Katznelson,…
We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. The construction involves an iteration procedure on an infinite-dimensional…