Related papers: Multipartite rational functions
Orthogonal rational functions (ORF) on the unit circle generalize orthogonal polynomials (poles at infinity) and Laurent polynomials (poles at zero and infinity). In this paper we investigate the properties of and the relation between these…
We apply the free product construction to various local algebras in algebraic quantum field theory. If we take the free product of infinitely many identical half-sided modular inclusions with ergodic canonical endomorphism, we obtain a…
We describe the problem of Sweedler's duals for bialgebras as essentially characterizing the domain of the transpose of the multiplication. This domain is the set of what could be called ``representative linear forms'' which are the…
A characterization of freeness for plane curves in terms of the Hilbert function of the associated Milnor algebra is given as well as many new examples of rational cuspidal curves which are free. Some stronger properties are stated as…
This paper examines fields of rationality in families of cuspidal automorphic representations of unitary groups. Specifically, for a fixed $A$ and a sufficiently large family $\mathcal{F}$, a small proportion of representations $\pi\in…
Let K be a skew field and (G,<) an ordered group. We show that the skew field generated by the group ring K[G] inside the Malcev-Neumann series ring K((G;<)) contains noncommutative free group algebras.
We introduce the notion of rationality for hyperholomorphic functions (functions in the kernel of the Cauchy-Fueter operator). Following the case of one complex variable, we give three equivalent definitions: the first in terms of…
Over an algebraically closed field of positive characteristic, there exist rational functions with only one critical point. We give an elementary characterization of these functions in terms of their continued fraction expansions. Then we…
Let X=H\G be a homogeneous spherical variety for a split reductive group G over the integers o of a p-adic field k, and K=G(o) a hyperspecial maximal compact subgroup of G=G(k). We compute eigenfunctions ("spherical functions") on X=X(k)…
An operator theoretic approach to orthogonal rational functions on the unit circle with poles in its exterior is presented in this paper. This approach is based on the identification of a suitable matrix representation of the multiplication…
Let H be an algebraic group scheme over a field k acting on a commutative k-algebra A which is a unique factorisation domain. We show that, under certain mild assumptions, the monoid of nonzero H-stable principal ideals in A is free…
We propose periodic Macdonald processes as a $(q,t)$-deformation of periodic Schur processes and a periodic analogue of Macdonald processes. It is known that, in the theory of stochastic processes related to a family of symmetric functions,…
We classify all possible extensions of a valuation from a ground field $K$ to a rational function field in one or several variables over $K$. We determine which value groups and residue fields can appear, and we show how to construct…
An algebra denoted $m\mathfrak{H}$ with three generators is introduced and shown to admit embeddings of the Hahn algebra and the rational Hahn algebra. It has a real version of the deformed Jordan plane as a subalgebra whose connection with…
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
Long before we learn to construct the field of rational numbers (out of the ring of integers) at university, we learn how to calculate with fractions at school. When it comes to "numbers", we are used to a commutative multiplication, for…
We study functions from a unique factorization monoid to a field. The set of all such functions is a commutative ring isomorphic to a ring of formal power series over the field, with indeterminates indexed by the prime elements of the…
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…
We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied…
An associative division algebra D is said to be _affine_ over a central subfield k if D is finitely generated as a k-algebra. In 1956 Amitsur famously proved that, when k is uncountable, D cannot be k-affine unless D is algebraic over k. In…