Abstract
In this paper, we discuss representation theorems for Mexican hat wavelet transform with determining function
α2(y) belonging to different class of functions. The classes
H,
A[p,q],
B[p,q], and
C[p,q] are characterized by the Mexican hat wavelet transform. Also, we investigate the convergence of the transform with its boundedness property. Furthermore, some representation theorems for locally bounded variation and locally Lebesgue integrable function are established.