Mathieu Subspaces of Univariate Polynomial Algebras

Abstract

We first give a characterization for Mathieu subspaces of univariate polynomial algebras over fields in terms of their radicals. We then deduce that for some classes of classical univariate orthogonal polynomials the Image Conjecture is true. We also prove two special cases of the one-dimensional Image Conjecture for univariate polynomial algebras $A[t]$ over commutative $\mathbb{Q}$-algebras $A$.

Latex, 22 pages

References in corpus (4)

• A Vanishing Conjecture on Differential Operators with Constant Coefficients
• On rational functions orthogonal to all powers of a given rational function on a curve
• Generalizations of the Image Conjecture and the Mathieu Conjecture
• Mathieu Subspaces of Associative Algebras

Cited by in corpus (4)

• Images of Ideals under Derivations and $\mathcal{E}$-Derivations of Univariate Polynomial Algebras over a Field of Characteristic Zero
• Mathieu Subspaces of Associative Algebras
• A Generalization of Mathieu Subspaces to Modules of Associative Algebras
• Analogue of the Duistermaat-van der Kallen Theorem for Group Algebras