You can query the pg_proc_info system catalog view to list all the user defined functions in a redshift database.
pg_proc_info view has information on all functions and stored procedures. prokind column has value ‘f’ for regular functions, ‘a’ for aggregate functions and ‘p’ for stored procedures.
select proname from pg_proc_info where prokind='f';
You can view the functions owned by a particular user by filtering on the proowner column.
select proname from pg_proc_info where prokind='f' and proowner='your_function_owner';