Hard to be explicit as there are many ways to ski this cat.
You can write some external script (say in PHP) to to make a REST call to pull the issues you want to close (you can write you own JQL query to be exactly as you want it) .. loop though the issues and make REST calls to close them. At least i think you can transition an issue via REST.
If you have scriptrunner or are familiar with writing services, this could be done there (that is where I do it). The concept is the same.
Using JIRA Command Line Interface (CLI), you can use something like the following in your favorite job scheduler:
jira --action runFromIssueList --jql "status = resolved AND resolutiondate < -1w" --common "--action transitionIssue --issue @issue@ --transition \"Close Issue\" "
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