  The aim of these two papers (I and II) is to try to give fundamental concepts
of quantum kinematics to q-deformed quantum spaces. Paper I introduces the
relevant mathematical concepts. A short review of the basic ideas of q-deformed
analysis is given. These considerations are continued by introducing q-deformed
analogs of Fourier transformations and delta functions. Their properties are
discussed in detail. Furthermore, q-deformed versions of sesquilinear forms are
defined, their basic properties are derived, and q-analogs of the
Fourier-Plancherel identity are proved. In paper II these reasonings are
applied to wave functions on position and momentum space.
