In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques in…
We investigate several topics related to the local behavior of functions: pointwise Hölder regularity, local scaling invariance and very oscillatory "chirp-like" behaviors. Our main tool is to relate these notions to two-microlocal conditions which are defined either on the Litt…
Maximal functions which measure the smoothness of a function are introduced and studied from the point of view of their relationship to classical smoothness and their use in proving embedding theorems, extension theorems, and various results on differentiation. New spaces of fun…
This paper is an important treatise on the theory of real functions. It is motivated by a study of Rogers and Taylor characterizing those interval functions which are absolutely continuous with respect to the [italic]s-dimensional Hausdorff measure. This leads naturally to inves…
