Operators {adjoint operator} {transposed operator} can find function scalar products, which are linear transformations from one function to another: (A(f1), f2). Adjoint operators can have inverses {self-adjointness}: (A(f1), f2) = (f1, A(f2)). The situation is analogous to the symmetric-integral-equation kernel. (T*f, g) = (f, T*g) and ||T*|| = ||T||, where T* is matrix-T transpose.
Adjoint-operator theory can apply to operators {Riesz operator} with form I - lambda * V, where lambda is parameter, I is identity operator, and V is complex continuous L^2-space operator.
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Date Modified: 2022.0225