FRACTIONAL SPECTRAL GRAPH WAVELET TRANSFORM APPROXIMATION IN TERMS OF MODULUS OF CONTINUITY

Abstract

In recent years, many wavelets formulas were constructed for vertices functionsof weighted graphs. In addition to the fractional wavelets, spectral graphs play importantrole in function approximation. In this paper, we define a fractional wavelet transforms interms of discrete graph Laplacian matrix. We study general properties of fractional spectralgraph wavelet transform (FRSGWT) in order to achieve the existence of best approximationof functions defined on vertices. Therefore, we prove direct and inverse theorems to getdegree of approximation with upper and lower bounds in terms of modulus of continuity.These theoretical results grantees that the approximation error implements well if appliedin various fields.