Divergence-free　wavelets　play　important　roles　in　both　partial　differential　equations　and　fluid　mechanics.　Many　constructions　of　those　wavelets　depend　usually　on　Hermite　splines.　We　study　several　types　of　convergence　of　the　related　Hermite　interpolatory　operators　in　this　paper.　More　precisely,　the　uniform　convergence　is　firstly　discussed　in　the　second　part;　then,　the　third　section　provides　the　convergence　in　the　Donoho＇s　sense.　Based　on　these　results,　the　last　two　parts　are　devoted　to　show　the　convergence　in　some　Besov　spaces,　which　concludes　the　completeness　of　Bittner　and　Urban＇s　expansions.