  Equivalence of partition functions for U(1) gauge theory and its dual in
appropriate phase spaces is established in terms of constrained hamiltonian
formalism of their parent action. Relations between the electric--magnetic
duality transformation and the (S) duality transformation which inverts the
strong coupling domains to the weak coupling domains of noncommutative U(1)
gauge theory are discussed in terms of the lagrangian and the hamiltonian
densities. The approach presented for the commutative case is utilized to
demonstrate that noncommutative U(1) gauge theory and its dual possess the same
partition function in their phase spaces at the first order in the
noncommutativity parameter \theta .
