The continuous fractional wavelet transform on w-type spaces

Abstract

An n-dimensional continuous fractional wavelet transform involving n-dimensional fractional Fourier transform is studied and its properties are obtained on Gel'fand and Shilov spaces of type WM(ℝn), WΩ(Cn) and W MΩ (Cn). It is shown that continuous fractional wavelet transform, W ψα φ WM(ℝn) → WM(ℝn×R+), W ψα φ: WΩ(Cn) → WΩ (Cn×R+) and W ψα φ: W MΩ (Cn) → W MΩ (Cn×R+) are linear and continuous maps, where ℝn and Cn are the usual Euclidean spaces. © Indian Mathematical Society, 2018.