… The methodology of fractal sets generates new procedures for the analysis of functions … of
fractal functions is described. The new mappings are perturbed versions of classical bases as …

… of fractal functions in L p -spaces, the following assumptions are inevitable: (i) base function
b … In Section 2, we reconsider the construction of fractal functions in L p -spaces, but from the …

… fractal Lp(I) functions from a given function in the same space. The existence of a Schauder
basis consisting of selfreferential functions in Lp spaces … the fractal analogues of some Lp(I) …

… approximation properties of fractal interpolation functions in the space of continuous functions
and Lp spaces. The … In our case M = Mα m(Λ), n = m and the functions fi are the basis of Mα …

… the fractal operator in more general spaces such as the space … the Lebesgue space Lp(I),
and in some standard spaces of … α-fractal operator, the existence of Schauder bases consisting …

… 3 Fractal bases for fractal functions 163 4 Recurrent sets as … relationship between certain
classes of smoothness spaces and the box dimension of the graphs of affine fractal functions. …

… A Hilbert basis of orthogonal fractal functions of this space is constructed explicitly. As a …
in terms of fractal mappings. Some conditions for the uniform convergence of the fractal series …

… bases of affine fractal … fractal basis for the same space with respect to a constant scale
vector α , independent of the function. The approach can be extended to Lebesgue spaces Lp …

… with our own desire to use this particular chapter as the basis for a course on IFS fractals. …
to the subject of fractal transforms on function and multifunction spaces. We often distinguish …

… and in particular we turn to the wavelet bases for some fractals, which have been constructed
in [… of the Besov spaces in terms of the coefficients of functions with respect to these bases. …