Tohoku Mathematical Journal
2018

December
SECOND SERIES VOL. 70, NO. 4

Tohoku Math. J.
70 (2018), 523-545

Title THE STRUCTURE OF THE SPACE OF POLYNOMIAL SOLUTIONS TO THE CANONICAL CENTRAL SYSTEMS OF DIFFERENTIAL EQUATIONS ON THE BLOCK HEISENBERG GROUPS: A GENERALIZATION OF A THEOREM OF KORÁNYI

Author Anthony C. Kable

(Received January 4, 2016, revised June 28, 2016)
Abstract. A result of Korányi that describes the structure of the space of polynomial solutions to the Heisenberg Laplacian operator is generalized to the canonical central systems on the block Heisenberg groups. These systems of differential operators generalize the Heisenberg Laplacian and, like it, admit large algebras of conformal symmetries. The main result implies that in most cases all polynomial solutions can be obtained from a single one by the repeated application of conformal symmetry operators.

Mathematics Subject Classification. Primary 35R03; Secondary 35C11, 22E25, 22E47.

Key words and phrases. Conformally invariant system, dual $b$-function identity, module of polynomial solutions, Heisenberg Laplacian.

To the top of this page

Back to the Contents