The phrase "an extensive study on" is correct and usable in written English.
You can use it when referring to a detailed and thorough examination or analysis of a particular subject or topic.
Example: "The researchers conducted an extensive study on the effects of climate change on marine biodiversity."
Alternatives: "a comprehensive analysis of" or "a thorough investigation into".
A book, recently published, contains an extensive study on the subject of the four day week.
It includes also an extensive study on possible interferences and on its elimination.
This paper presents initial results from an extensive study on the calculation of the surface free energy of mineral materials.
She added that it was frustrating to be unable to do an extensive study on gun violence while she was there.
In conjunction with the ACIR, the Lowenstein Clinic conducted an extensive study on the links between companies operating in Sudan and the ongoing genocide in the country.
In the past year, the Army has conducted an extensive study on the economic impacts of the reductions and held community meetings across the country.
This paper presents an extensive study on structural behaviour of archaeological building remains in Peru, based on in-situ non-destructive testing as well as on numerical approaches.
This paper presents an extensive study on the experimental and numerical investigation of metal layered interply hybrid composites subjected to low velocity impact.
The present investigation reports an extensive study on the grain refinement and the defect structure in the pulsed electrodeposited nanocrystalline copper.
Around the same time Sablon commissioned the University of Louvain to carry out an extensive study on youth football in Belgium, which involved filming 1,500 matches across different age groups.
However, there has not been an extensive study on the abundance of shape analysis techniques in the context of pose discrimination.
