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The phrase "further analysis on" is correct and usable in written English.
You could use it to introduce a topic that needs to be explored in greater detail. For example, "This report provides an overview of the current state of the industry, but further analysis on regional trends will be necessary to gain a more comprehensive understanding."
Exact(60)
Further analysis on the core was performed to evaluate one of the causes of LRP we presented.
It intends to do further analysis on whether banks should be held responsible and shift the burden away from consumers.
Further analysis on cardiovascular effects is pending.
Hasanah et al. (2015a) conducted further analysis on this topic.
Further analysis on attrition is conducted in the following section.
Update: Given Index is London-based, there's further analysis on TechCrunch UK.
Further analysis on the stabilization mechanism was conducted.
So, we will focus our further analysis on the second (τ 2, I 2) component alone.
This is followed by further analysis on the states with a large population density.
For accommodating further analysis on this variable, we decided to split students' data into two groups.
Further analysis on the RNA level is necessary for clarification and validation of this contention.
More suggestions(15)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com