Invariant bilinear differential operators

Translation-invariant bilinear operators with positive kernels

We study L (or Lr,∞) boundedness for bilinear translation-invariant operators with nonnegative kernels acting on functions on R. We prove that if such operators are bounded on some products of Lebesgue spaces, then their kernels must necessarily be integrable functions on R, while via a counterexample we show that the converse statement is not valid. We provide certain necessary and some suffic...

Invariant differential operators

on the complex upper half-plane H, provably invariant under the linear fractional action of SL2(R), but it is oppressive to verify this directly. Worse, the goal is not merely to verify an expression presented as a deus ex machina, but, rather to systematically generate suitable expressions. An important part of this intention is understanding reasons for the existence of invariant operators, a...

Invariant Differential Operators On

For two positive integers m and n, we let Pn be the open convex cone in R consisting of positive definite n × n real symmetric matrices and let R be the set of all m×n real matrices. In this article, we investigate differential operators on the non-reductive manifold Pn × R (m,n) that are invariant under the natural action of the semidirect product group GL(n,R)⋉R on the MinkowskiEuclid space P...

Invariant Bilinear Differential Pairings on Parabolic Geometries

Invariant Theory and Differential Operators

Constructive invariant theory was a preoccupation of many nineteenth century mathematicians, but the topic fell out of fashion in the early twentieth century. In the latter twentieth century the topic enjoyed a resurgence, partly due to its connections with the construction of moduli spaces in algebraic geometry and partly due to the development of computational algorithms suitable for implemen...