Related papers: On the application of the factorized Fueter-Sce ma…
Octonionic analysis is becoming eminent due to the role of octonions in the theory of G2 manifold. In this article, a new slice theory is introduced as a generalization of the holomorphic theory of several complex variables to the…
A general two-dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Applying the generators of the closed subalgebra generated by…
In this paper, we build on the work of [T. Hughes, G. Sangalli, VARIATIONAL MULTISCALE ANALYSIS: THE FINE-SCALE GREENS' FUNCTION, PROJECTION, OPTIMIZATION, LOCALIZATION, AND STABILIZED METHODS, SIAM Journal of Numerical Analysis, 45(2),…
The paper is about methods of discrete Fourier analysis in the context of Weyl group symmetry. Three families of class functions are defined on the maximal torus of each compact simply connected semisimple Lie group $G$. Such functions can…
In this paper we introduce a generalization of theta series in the context of the slice monogenic function theory in $\mathbb{R}^{n+1}$ where me make use of the so-called $*$-exponential function in a hypercomplex variable. Together with…
Along with the development of the theory of slice regular functions over the real algebra of quaternions $\mathbb{H}$ during the last decade, some natural questions arose about slice regular functions on the open unit ball $\mathbb{B}$ in…
We give a complete classification of conformally covariant differential operators between the spaces of $i$-forms on the sphere $S^n$ and $j$-forms on the totally geodesic hypersphere $S^{n-1}$. Moreover, we find explicit formul{\ae} for…
The known Complex Step Derivative (CSD) method allows easy and accurate differentiation up to machine precision of real analytic functions by evaluating them a small imaginary step next to the real number line. The current paper proposes…
Coalgebras for an endofunctor provide a category-theoretic framework for modeling a wide range of state-based systems of various types. We provide an iterative construction of the reachable part of a given pointed coalgebra that is inspired…
We extend a factorization due to Krein to arbitrary analytic functions from the upper half-plane to itself. The factorization represents every such function as a product of fractional linear factors times a function which, generally, has…
We provide a coherent overview of a number of recent results obtained by the authors in the theory of schemes defined over the field with one element. Essentially, this theory encompasses the study of a functor which maps certain geometries…
A Schur-class function in $d$ variables is defined to be an analytic contractive-operator valued function on the unit polydisk. Such a function is said to be in the Schur--Agler class if it is contractive when evaluated on any commutative…
The focus of this article is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of…
By appropriate choices of elements in the underlying iterated function system, methodology of fractal interpolation entitles one to associate a family of continuous self-referential functions with a prescribed real-valued continuous…
The aim of this paper is to provide and prove the most general Cauchy integral formula for slice regular functions and for C^1 functions on a real alternative *-algebra. Slice regular functions represent a generalization of the classical…
A standard technique for producing monogenic functions is to apply the adjoint quaternionic Fueter operator to harmonic functions. We will show that this technique does not give a complete system in L2 of a solid torus, where toroidal…
A consistent factorization theorem is presented in the framework of effective field theories. Conventional factorization suffers from infrared divergences in the soft and collinear parts. We present a factorization theorem in which the…
We give a factorization procedure for a strictly hyperbolic partial differential operator of second order with logarithmic slow scale coefficients. From this we can microlocally diagonalize the full wave operator which results in a coupled…
We introduce an algorithm to compute the functions belonging to a suitable set ${\mathscr F}$ defined as follows: $f\in {\mathscr F}$ means that $f(s,x)$, $s\in A\subset {\mathbb R}$ being fixed and $x>0$, has a power series expansion…
In some applications, one is interested in reconstructing a function $f$ from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we…