Properties of multilinear fractional wavelet transforms in some function spaces

This thesis consist of four chapters. In the first part, the literature summary of the thesis topic is given, and in the second part, the fundamental definitions and theorems we use in the thesis are stated. In the third section where the findings are included, firstly, the relationship between the multilinear fractional wavelet transform and the fractional multilinear Fourier transform is given, and a new orthogonality relation for this transform is proven. Afterwards, the adjoint operator of the fractional multilinear wavelet transform is found. Additionally, multilinear fractional wavelet transform and continuity (boundedness) of the adjoint operator in various function spaces are examined. Finally, the importance of this transformation in n- dimensional smooth spaces is investigated