• Corpus ID: 119253712

A Noncommutative Mikusinski Calculus

  title={A Noncommutative Mikusinski Calculus},
  author={Markus Rosenkranz and Anja Korporal},
  journal={arXiv: Rings and Algebras},
We set up a left ring of fractions over a certain ring of boundary problems for linear ordinary differential equations. The fraction ring acts naturally on a new module of generalized functions. The latter includes an isomorphic copy of the differential algebra underlying the given ring of boundary problems. Our methodology employs noncommutative localization in the theory of integro-differential algebras and operators. The resulting structure allows to build a symbolic calculus in the style of… 
1 Citations

On De Graaf spaces of pseudoquotients

A space of pseudoquotients $\mathcal{B}(X,S)$ is defined as equivalence classes of pairs $(x,f)$, where $x$ is an element of a non-empty set $X$, $f$ is an element of $S$, a commutative semigroup of



Symbolic Analysis for Boundary Problems: From Rewriting to Parametrized Gröbner Bases

The canonical simplifier for integro-differential polynomials is used for generating an automated proof establishing a canonical simplifiers for integrospecific operators in the Theorema system.

A skew polynomial approach to integro-differential operators

It is shown how skew polynomials can be used for defining the integro-differential Weyl algebra as a natural extension of the classical Weylgebra in one variable as well as for fixing the integration constant.


A Baxter algebra is a commutative algebra A that carries a generalized integral operator. In the first part of this paper we review past work of Baxter, Miller, Rota and Cartier in this area and

Noncommutative localization in noncommutative geometry

The aim of these notes is to collect and motivate the basic localization toolbox for the geometric study of ``spaces'', locally described by noncommutative rings and their categories of one-sided

Galois Theory of Linear Differential Equations

Linear differential equations form the central topic of this volume, Galois theory being the unifying theme. A large number of aspects are presented: algebraic theory especially differential Galois

Baxter Algebras and the Umbral Calculus

We apply Baxter algebras to the study of the umbral calculus. We give a characterization of the umbral calculus in terms of Baxter algebra. This characterization leads to a natural generalization of

An algebraic foundation for factoring linear boundary problems

Motivated by boundary problems for linear differential equations, we define an abstract boundary problem as a pair consisting of a surjective linear map (“differential operator”) and an orthogonally

Free Ideal Rings and Localization in General Rings

Preface Note to the reader Terminology, notations and conventions used List of special notation 0. Preliminaries on modules 1. Principal ideal domains 2. Firs, semifirs and the weak algorithm 3.

Integro-differential polynomials and operators

Two algebraic structures for treating integral operators in conjunction with derivations are proposed that can be used to solve boundary problems for linear ordinary differential equations and canonical/normal forms with algorithmic simplifiers are described.