As the name suggests, password based key derivation functions are used for deriving a cryptographic key from, well, a password.
Is there any use for PBKDFs with empty password? Does it give any advantage over simple hash or HMAC? More specifically, in the case of PBKDF2-HMAC it would mean applying HMAC with an empty key, simplifying it to a double hash.
For example, according to its documentation, OpenSSL allows calling
PKCS5_PBKDF2_HMAC() with no password given, but RFC 6070 does not define test vectors for empty passwords (which IMHO would be an important edge case for test vectors).