---
res:
bibo_abstract:
- "Abstract\r\n Let \r\n
\ \r\n $$\\mu $$\r\n
\ \r\n
\ μ\r\n \r\n \r\n
\ be a radial compactly supported distribution
on a harmonic NA group. We prove that the right convolution
operator \r\n \r\n $$c_{\\mu
}:f \\mapsto f* \\mu $$\r\n \r\n
\ \r\n \r\n c\r\n
\ μ\r\n \r\n
\ :\r\n f\r\n
\ ↦\r\n f\r\n
\ \r\n ∗\r\n
\ μ\r\n \r\n \r\n
\ \r\n maps
the space of smooth \r\n \r\n
\ $$\\mathfrak {v}$$\r\n \r\n v\r\n
\ \r\n \r\n -radial
functions onto itself if and only if the spherical Fourier transform \r\n
\ \r\n $$\\widetilde{\\mu
}(\\lambda )$$\r\n \r\n
\ \r\n \r\n μ\r\n
\ ~\r\n \r\n
\ \r\n (\r\n
\ λ\r\n )\r\n
\ \r\n \r\n \r\n
\ \r\n , \r\n
\ \r\n $$\\lambda
\\in \\mathbb {C}$$\r\n \r\n
\ \r\n λ\r\n ∈\r\n
\ C\r\n \r\n \r\n
\ \r\n , is slowly
decreasing. As an application, we prove that certain averages over spheres are
surjective on the space of smooth \r\n \r\n
\ $$\\mathfrak {v}$$\r\n \r\n v\r\n
\ \r\n \r\n -radial
functions.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Efthymia
foaf_name: Papageorgiou, Efthymia
foaf_surname: Papageorgiou
foaf_workInfoHomepage: http://www.librecat.org/personId=100325
bibo_doi: 10.1007/s12220-024-01837-w
bibo_issue: '1'
bibo_volume: 35
dct_date: 2024^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/1050-6926
- http://id.crossref.org/issn/1559-002X
dct_language: eng
dct_publisher: Springer Science and Business Media LLC@
dct_title: Surjectivity of Convolution Operators on Harmonic NA Groups@
...