This paper shows an example of developing a fusion system in a formal framework, i.e., through the use of formal operators in the development process.
We finally provide formal operators for integrating systems and show that they are consistent with the classical definitions of those operators on transfer functions which model real systems.
and its formal adjoint operator (the Hodge codifferential operator) (1.5).
Its formal adjoint operator is given by on,.
Its formal adjoint operator is defined by (2.6).
Two factorisations of the formal difference operator,, associated with (1.1), are given.
We show that, for 1⩽pformal inclusion operator from Jp to Jq is finitely strictly singular.
Its formal adjoint operator d⋆ which is called the Hodge codifferential is defined by d⋆ = (-1)nl+1⋆ d⋆: D'(Ω, ∧l+1) → D'(Ω, ∧ l ), where l = 0, 1,⋯, n - 1, and ⋆ is the well known Hodge star operator.
and its formal adjoint operator d ∗ = ( − 1 ) n l + 1 ∗ d ∗ : C ∞ ( Ω, ∧ l + 1 ) → C ∞ ( Ω, ∧ l ), known as the Hodge codifferential, where the symbol ∗ denotes the Hodge star duality operator.
By (X^{ast}=(X_{1}^{ast},X_{2}^{ast},ldots,X_{m}^{ast})) we denote the formal adjoint operator to X. Let Ω be a bounded open set of (mathbb{R}^{n}) for (ngeq2).
