Threads, introspection, sharing of :memory: databases

I'm using pysqlite in some multi-threaded software.  All I need is the
:memory:database.  If I understand the errors I've received thusfar, I can't
share a single connection in multiple threads.  Accordingly, I need

    self.connection = sqlite3.connect(":memory:")

in each thread.  If I execute that in different threads is one ini-memory
database created which is shared across all threads?

Let's assume that's the case.  I then need to create tables, e.g.:

    cursor = self.connection.cursor()
    cursor.execute("create table foo ...")
    cursor.commit()

Executing that multiple times in the same thread yields an OperationalError.
Is there not some way of introspecting the database for its tables, or do I
just have to catch the exception?

Thanks,

Skip Montanaro