The n-dimensional continuous wavelet transformation on Gelfand and Shilov type spaces

Abstract

In this paper the wavelet transformationon Gelfand and Shilov spaces of type WM(⬛n), WΩ(Δn) and WMΩ(Δn) is studied. It is shown that Wψφ : WM(⬛n) → WM(⬛n×⬛+n), Wψφ : WΩ(Δn) →WΩ(Δn×⬛+n) and Wψφ : WMΩ(Δn) →WMΩ(Δn×⬛+n) is linear andcontinuous where ⬛n and Δn are n-dimensional realnumbers and complex numbers. A boundedness result in a generalized Sobolev space is derived.

Keywords

• Continuous wavelet transformation
• Sobolev space
• Fourier transformation
• W-spaces.