Arens , R . Operational calculus of linear relations . Pacific J. Math . 11 , 1 ( 1961 ), 9 – 23 .  Kato , T . Trotter’s product formula for an arbitrary pair of self-adjoint contraction semigroups . In Topics in Functional
The notion of Hankel operators associated with analytic crossed products were introduced and researched in . In this paper,
we study the adjoint of Hankel operators and give necessary and sufficient condition that the adjoint of a Hankel operator
is again a Hankel operator.
The Hodge–de Rham Theorem is introduced and discussed. This result has implications for the general study of several partial differential equations. Some propositions which have applications to the proof of this theorem are used to study some related results concerning a class of partial differential equation in a novel way.