Wavelet methods in classical and functional analysis

The project aims to develop new wavelet tool in the analysis of various problems from classical and functional analysis. Our specific objectives are to:
• Reveal the multifractal nature of lacunary Fourier series from classical analysis.
• Give a wavelet description of ultradifferentiability.
• Characterize generalized Besov spaces in terms of the wavelet transform.
• Obtain applications in regularity theory for Colombeau generalized functions.