What is the correct preposition to use?

Hello everyone

Here is my question: I don't know which preposition I should use in the following sentence.

The context is the following: a search function can search files that log information. You can use parameters (Starting/Ending date and Starting/Ending time) to restrict the search to the defined interval of time.

Now, which preposition should I use:

"If no starting and ending times are specified, the search will be performed <???> the entire interval defined by the starting/ending dates"

Should it be "over", "for", "on" or even something else?

I hope it makes sense. Thanks for any help.