Asymptotic analysis of fundamental solutions of hypoelliptic operators

Eugene Shargorodsky, George Chkadua*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Asymptotic behavior at infinity is investigated for fundamental solutions of a hypoelliptic partial differential operator P(i∂ x) = (P 1(i∂ x)) m 1 · · · (P l(i∂ x)) ml with the characteristic polynomial that has real multiple zeros. Based on asymptotic expansions of fundamental solutions, asymptotic classes of functions are introduced and existence and uniqueness of solutions in those classes are established for the equation P(i∂ x)u = f in ℝ n. The obtained results imply, in particular, a new uniqueness theorem for the classical Helmholtz equation.

Original languageEnglish
Pages (from-to)205-228
Number of pages24
JournalGeorgian Mathematical Journal
Issue number2
Early online date27 Oct 2023
Publication statusPublished - 1 Apr 2024


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