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Theory and Modern Applications

Table 1 Some functions and their annihilators

From: Hahn difference equations in Banach algebras

Function

Annihilator

\(x\in\mathbb{X}\)

\(D_{q,\omega}\)

\(xt^{n}\)

\(D_{q,\omega}^{n+1}\)

\(e_{A}(t)\)

\(D_{q,\omega}-A(t) \)

\(\cos_{q,\omega}(A,t)\)

\(D_{q,\omega}^{2}+A^{2}\)

\(\sin_{q,\omega}(A,t)\)

\(D_{q,\omega}^{2}+A^{2}\)