For functions f on the discrete circle {0,…,N-1} this program computes their uncentered maximal functions and the ratio of the L^p norms of the kth derivative of the maximal function and the function.

Building

If git is installed you can fetch the repository using

git clone https://cgit.jnwt.eu/discretemf

The program is written in C and hence requires a C compiler for building. If make and gcc are installed then running

make

builds three files:

• charf_approx does computations using floating point (double) numbers, which come with rounding errors.
• charf_error does computations using floating point (double) numbers and gives an upper bound for the total rounding error.
• charf_exact does exact computations using fractions. Nominator and denominator are of type unsigned long long and bounded in size accordingly.

Correctness

I am relatively confident that the error bounds are correct for all operations except exponentiation, which is not used for p∈{1,∞}.