TY - JOUR
T1 - Asymptotic analysis of fundamental solutions of hypoelliptic operators
AU - Shargorodsky, Eugene
AU - Chkadua, George
N1 - Publisher Copyright:
© 2023 the author(s), published by De Gruyter.
PY - 2024/4/1
Y1 - 2024/4/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85176250097&partnerID=8YFLogxK
U2 - 10.1515/gmj-2023-2072
DO - 10.1515/gmj-2023-2072
M3 - Article
SN - 1072-947X
VL - 31
SP - 205
EP - 228
JO - Georgian Mathematical Journal
JF - Georgian Mathematical Journal
IS - 2
ER -