A note on irregular wavelet frames

In this note, we give a necessary condition for irregular wavelet frames, which extends the results of Chui and Shi. We prove that if the system {@j"m","n@?s"m^-^1^/^2@js"m^-^1.-t"n}"m","n"@?"Z constitute a frame for L^2(R) with frame bounds A, B, then @?"m"@?"Z|@j@?(s"m@x)|^2 is bounded up and below. Moreover, the upper and lower bounds depend only on the frame bounds A, B and density of the samples t"n's, not rely on the samples s"m's and the specific generator function @j however.