Zobrazeno 1 - 10
of 93
pro vyhledávání: '"Rosenkranz, Markus"'
Autor:
Landsmann, Günter, Rosenkranz, Markus
We introduce a general class of Heisenberg groups motivated by applications of algebraic Fourier theory. Basic properties are examined from a homological perspective.
Comment: 64 pages
Comment: 64 pages
Externí odkaz:
http://arxiv.org/abs/2106.15672
Autor:
Rosenkranz, Markus, Landsmann, Günter
The notion of Fourier transformation is described from an algebraic perspective that lends itself to applications in Symbolic Computation. We build the algebraic structures on the basis of a given Heisenberg group (in the general sense of nilquadrati
Externí odkaz:
http://arxiv.org/abs/2009.12198
Autor:
Rosenkranz, Markus, Serwa, Nitin
Publikováno v:
An integro-differential structure for Dirac distributions 2019
We develop a new algebraic setting for treating piecewise functions and distributions together with suitable differential and Rota-Baxter structures. Our treatment aims to provide the algebraic underpinning for symbolic computation systems handling s
Externí odkaz:
http://arxiv.org/abs/1707.06591
Publikováno v:
International Journal of Algebra and Computation, 28 (2018), 1-36
Using the language of operated algebras, we construct and investigate a class of operator rings and enriched modules induced by a derivation or Rota-Baxter operator. In applying the general framework to univariate polynomials, one is led to the integ
Externí odkaz:
http://arxiv.org/abs/1512.01247
Publikováno v:
Joural Algebra and Its Applications, 18 (2019), 1950207, 51pp
We set up an algebraic theory of multivariable integration, based on a hierarchy of Rota-Baxter operators and an action of the matrix monoid as linear substitutions. Given a suitable coefficient domain with a bialgebra structure, this allows us to bu
Externí odkaz:
http://arxiv.org/abs/1503.01694
Publikováno v:
Pacific J. Math. 275 (2015) 481-507
Rota-Baxter operators are an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota-Baxter operators and integrals in the case of the polynomial algebra $\mathbf{k}[x]$. We consider two class
Externí odkaz:
http://arxiv.org/abs/1407.5306
Publikováno v:
Communications in Algebra, 47 (2019), 3094-3116
In this paper we determine all the Rota-Baxter operators of weight zero on semigroup algebras of order two and three with the help of computer algebra. We determine the matrices for these Rota-Baxter operators by directly solving the defining equatio
Externí odkaz:
http://arxiv.org/abs/1402.3702
Publikováno v:
Journal of Algebra, 442 (2015) 354-396
The notion of commutative integro-differential algebra was introduced for the algebraic study of boundary problems for linear ordinary differential equations. Its noncommutative analog achieves a similar purpose for linear systems of such equations.
Externí odkaz:
http://arxiv.org/abs/1402.1890
Autor:
Rosenkranz, Markus, Phisanbut, Nalina
We introduce a general algebraic setting for describing linear boundary problems in a symbolic computation context, with emphasis on the case of partial differential equations. The general setting is then applied to the Cauchy problem for completely
Externí odkaz:
http://arxiv.org/abs/1304.7380
Publikováno v:
Journal of Pure and Applied Algebra 218 (2014), 456-471
The concept of integro-differential algebra has been introduced recently in the study of boundary problems of differential equations. We generalize this concept to that of integro-differential algebra with a weight, in analogy to the differential Rot
Externí odkaz:
http://arxiv.org/abs/1212.0266