Related papers: Complex Iterations and Bounded Analytic Hyper-oper…
A complex-analytic structure within the unit disk of the complex plane is presented. It can be used to represent and analyze a large class of real functions. It is shown that any integrable real function can be obtained by means of the…
We give a particular choice of the higher Eilenberg-MacLane maps by a recursive formula.This choice leads to a simple description of the homotopy operations for simplicial Z/2-algebras.
In this paper, an open problem in the multidimensional complex analysis is pesented that arises in the investigation of the regularity properties of Fourier integral operators and in the regularity theory for hyperbolic partial differential…
This article summarises the theory of several bounded functional calculi for unbounded operators that have recently been discovered. The extend the Hille--Phillips calculus for (negative) generators $A$ of certain bounded $C_0$-semigroups,…
We study a natural extension to complex numbers of the standard continued fractions. The basic algorithm is due to Lagrange and Gauss, though it seems to have gone mostly unnoticed as a way to create continued fractions. The new…
It is possible to perform some operations with extrafunctions applying these operations separately to each coordinate. Operations performed in this manner are called regular. It is proved that it is possible to extend several operations…
While the asymptotic Borel mapping, sending a function into its series of asymptotic expansion in a sector, is known to be surjective for arbitrary openings in the framework of ultraholomorphic classes associated with sequences of rapid…
We introduce a new approach for the study of the Problem of Iterates using the theory on general ultradifferentiable structures developed in the last years. Our framework generalizes many of the previous settings including the Gevrey case…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
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…
Learned image reconstruction has become a pillar in computational imaging and inverse problems. Among the most successful approaches are learned iterative networks, which are formulated by unrolling classical iterative optimisation…
We introduce a hierarchy of fast-growing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a non-elementary…
We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions. Our algorithms exploit the combinatorial properties of the Jack function, and have…
We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…
By using nonstandard analysis, and in particular iterated hyper-extensions, we give foundations to a peculiar way of manipulating ultrafilters on the natural numbers and their pseudo-sums. The resulting formalism is suitable for…
We revisit and extend known bounds on operator-valued functions of the type $$ T_1^{-z} S T_2^{-1+z}, \quad z \in \ol \Sigma = \{z\in\bbC\,|\, \Re(z) \in [0,1]\}, $$ under various hypotheses on the linear operators $S$ and $T_j$, $j=1,2$.…
In this paper we describe an iterative operator-splitting method for unbounded operators. We derive error bounds for iterative splitting methods in the presence of unbounded operators and semigroup operators. Here mixed applications of…
We introduce a set of special functions called multiple polyexponential integrals, defined as iterated integrals of the exponential integral $\text{Ei}(z)$. These functions arise in certain perturbative expansions of the local solutions of…
This paper studies the design of programming languages with handlers of higher-order effectful operations -- effectful operations that may take in computations as arguments or return computations as output. We present and analyse a core…
We show that the discrete complex, and numerous hypercomplex, Fourier transforms defined and used so far by a number of researchers can be unified into a single framework based on a matrix exponential version of Euler's formula…