You don’t need to put your code in your theme functions. This needs to be a custom page template. Learn about page templates here:
http://codex.wordpress.org/Page_Templates
Your code is custom loop so you need to also learn about loops and then using WP_Query so next stop will be here:
http://codex.wordpress.org/The_Loop
Then read this page:
http://codex.wordpress.org/Class_Reference/WP_Query
After you do this you will be ready to implement your custom loop to show authors their posts.
Study, the codex so that you have a better understanding of how WordPress works before you make changes to things that will break WordPress.
Then when you ask questions here you will be able to get a better answer to problems that you are having because the people here will understand your question better.
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