My friend's Ed book

This is correct:

This is my friend Ed's book.

The noun phrase my friend Ed's functions as a determiner.

Aspara GusThis is correct:This is my friend Ed's book. The noun phrase my friend Ed's functions as a determiner.

Is the determiner a closed word class or a function in the noun phrase?

Is "my friend Ed's" a genitive phrase functioning as a premodifier of the head word "book"?

AnonymousIs the determiner a closed word class or a function in the noun phrase?

It's the function of the noun phrase. In my grammar ‘determinative’ is a word class, and ‘determiner’ is a function in NP structure (in some grammars it's the other way around), which may be filled by a determiner / determinative phrase or a genitive NP.

Aspara GusIt's the function of the noun phrase. In my grammar ‘determinative’ is a word class, and ‘determiner’ is a function in NP structure (in some grammars it's the other way around), which may be filled by a determiner / determinative phrase or a genitive NP.

Thanks for the reply. Nevertheless, I'm still none the wiser.

Many grammarians use the word determiner of the closed class that you refer to, which includes such words as such words as a, the, this, these, many. However some use the word determinative of this closed class. They use the word determiner of other words and phrases which are not (in their stem) determiners, but which function as such.