Related papers: Integration with filters
Using a concept of filter we propose one generalization of Riemann integral, that is integration with respect to filter. We study this problem, demonstrate different properties and phenomena of filter integration.
This paper addresses the natural question: ``How should frames be compared?'' We answer this question by quantifying the overcompleteness of all frames with the same index set. We introduce the concept of a frame measure function: a…
For a general class of non-negative functions defined on integral ideals of number fields, upper bounds are established for their average over the values of certain principal ideals that are associated to irreducible binary forms with…
We construct a new kind of measures, called projection families, which generalize the classical notion of vector and operator-valued measures. The maximal class of reasonable functions admits an integral with respect to a projection family,…
Intuitively, the filter dimension of an algebra or a module measures how `close' standard filtrations of the algebra or the module are. In particular, for a simple algebra it also measures the growth of how `fast' one can prove that the…
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…
An integral in the sense of principal value of a singular function or of product of singular functions can appear itself as a singular function in some range of values of integration parameters. In this case, if necessary subsequently to…
This paper studies the concept of algorithmic equiresolution of a family of embedded varieties or ideals, which means a simultaneous resolution of such a family compatible with a given (suitable) algorithm of resolution in characteristic…
In this article, numerical integration is formulated as evaluation of a matrix function of a matrix that is obtained as a projection of the multiplication operator on a finite-dimensional basis. The idea is to approximate the continuous…
Some properties of integral averages of functions on intervals and their asymptotic behavior are investigated. The results are aimed at applications to entire and subharmonic functions.
In this paper we extend the idea of integration to generic algebras. In particular we concentrate over a class of algebras, that we will call self-conjugated, having the property of possessing equivalent right and left multiplication…
Based on the total integrability we first define an integral of a real valued function f as an interval function associated to its antiderivative F. By introducing the concept of the residue of a function into the real analysis, the…
We express multiplicities and degree functions of graded families of $\mathfrak{m}_R$-primary ideals in an excellent normal local ring $(R,\mathfrak{m}_R)$ as limits of intersection products. Moreover, in dimension 2, we show more refined…
In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the definition of residues and integral function element, we obtain the…
The problem of quantizing theories defined over configuration spaces described by non-commuting parameters is considered. In this paper we describe the first step in this direction, that is the definition of an integral over a general…
We extend the asymptotic Samuel function of an ideal to a filtration and show that many of the good properties of this function for an ideal are true for filtrations. There are, however, interesting differences, which we explore. We study…
Let $X$ be a complete measure space of finite measure. The Lebesgue transform of an integrable function $f$ on $X$ encodes the collection of all the mean-values of $f$ on all measurable subsets of $X$ of positive measure. In the problem of…
This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…
An algebraic integer is said large if all its real or complex embeddings have absolute value larger than $1$. An integral ideal is said \emph{large} if it admits a large generator. We investigate the notion of largeness, relating it to some…
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…