The purpose of this papem is not to present new results,
but to make a little-known area in the mathematical
foundations of quantum mechanics accessable to a wider audience. ~
Therefore the discussion of the physics and mathematics
will be limited to the bare essentials. The whole subject
is developed in Terms of the simple, well-known example of the
harmonic oscillator, and the mathematical notions have been
introduced in the least general form which is compatible with
the purpose of This paper (Unfortunately, the mathematics
had to be abbreviated to an extent which, in The second
part, precludes the possibility of proving The mathematical
statements, but which, hopefully, still allows one to
understand the content of These mathematical statements). After