Fractional wavelet transform and some properties

Our thesis consists of five parts. A summary of the literature on the subject of the thesis is given in the first chapter, and basic definitions and theorems that we use in the thesis are given in the second chapter. In the third chapter, wavelet transform and some ıts propertles are mentioned. In the fourth chapter, the definition and characteristics of fractional wavelet transform are discused. In the five part of the fifth chapter, the vector space (〖FW〗_(ω_1 ω_2)^(θ,p,q) )_a (R)={f∈L_(ω_1)^p (R)│W_ψ^θ f∈L_(ω_2)^q (R) } , (1≤p,q<∞,ψ∈S(R)) are defined where ω_1,ω_2 are two weight functions on R and a∈R^+ is a fixed number. Also for f∈(〖FW〗_(ω_1 ω_2)^(θ,p,q) )_a (R), the norm ‖f‖_((〖FW〗_(ω_1 ω_2)^(θ,p,q) )_a )=‖f‖_(p,ω_1 )+‖W_ψ^θ f‖_(q,ω_2 ) is placed in this space. Then it is found that this space is Banach space and it is invariant under translation and modulation operators. Also it has been proved part (〖FW〗_(ω_1 ω_2)^(θ,p,q) )_a (R) space is dense in the space L_(ω_1)^p (R) . In the second part of the findings section, the dual space of the space (〖FW〗_(ω_1 ω_2)^(θ,p,q) )_a (R) is mentioned. The third part of the findings section, the inelusion propertles of space of (〖FW〗_(ω_1,ω_2)^(θ,p,q) )_a (R), are investigated.