Rational Hadamard products via Quantum Diagonal Operators
G\'erard Henry Edmond Duchamp (LIPN), Silvia Goodenough (LIPN), Karol, A. Penson (LPTMC)
TL;DR
This paper explores the properties of the Hadamard product in the algebra of rational functions using quantum diagonal operators, providing explicit formulas and stability results.
Contribution
It introduces a novel approach using Bargmann-Fock representation to analyze Hadamard products via quantum diagonal operators, with explicit multiplication formulas.
Findings
Stability of periodic functions under Hadamard product
Explicit formulas for multiplication in rational function algebra
Connection between quantum operators and Hadamard product properties
Abstract
We use the remark that, through Bargmann-Fock representation, diagonal operators of the Heisenberg-Weyl algebra are scalars for the Hadamard product to give some properties (like the stability of periodic fonctions) of the Hadamard product by a rational fraction. In particular, we provide through this way explicit formulas for the multiplication table of the Hadamard product in the algebra of rational functions in .
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Advanced Topics in Algebra