The phrase "acknowledged influence" is correct and usable in written English.
It can be used when referring to a recognized or accepted impact that someone or something has had on a particular subject or area.
Example: "The acknowledged influence of classical music on modern compositions cannot be overlooked."
Alternatives: "recognized impact" or "accepted effect".
Laughing Clowns were a band unparalleled in Australian rock history, contemporaries of the Triffids, the Go-Betweens, the Birthday Party and the Moodists, with a clear (acknowledged) influence on all.
Hugely iconic in the 1980s and a major, acknowledged influence on the emerging Radiohead and Coldplay, the Bunnymen found themselves having to finance their recent, 11th studio album, Meteorites, via fan-funding site PledgeMusic.
Their results, which consider other factors such as education, physical health, genetic variation, IQ, self-esteem and current happiness, show that the effect of individual happiness on income is greater than the widely acknowledged influence of income on happiness.
My current favourite comes from the pen of Jean-Luc Godard, an inexhaustible source of anti-American sentiment (despite, it must be said, the profound and openly acknowledged influence of Hollywood on his films).
An acknowledged influence on rap artists Ice-T and Ice Cube, Slim also provided a glossary here, including pull coat ("to inform or alert") and peckerwood ("contemptuous term referring to white men").
Auster likes to explicate his own texts, overtly stating his themes in the very books that embody them, but one rarely acknowledged influence is the legacy of the Second World War.
Bergman, Eliot's Four Quartets and Vermeer are among Davies's acknowledged influences.
Two of Mr. Mathews's longest-lasting associations were with the saxophonist Johnny Griffin, from 1978 to 1982, and the drummer T. S. Monk — son of the pianist and composer Thelonious Monk, one of Mr. Mathews's acknowledged influences — for most of the 1990s.
The band's music takes cues from Japanese noise rock bands such as Boredoms and Ruins, although composers Philip Glass and Sun Ra are acknowledged influences.
In contrast, 'careers advice' and the influence of 'family' and 'friends' were the least commonly acknowledged influences on respondents' choice of dentistry.
A weakness of many ecological models is lack of specificity about which of the many acknowledged influences are most important [ 58].
