  In this article we construct a maximal set of kernels for a multi-parameter
linear scale-space that allow us to construct trees for classification and
recognition of one-dimensional continuous signals similar the Gaussian linear
scale-space approach. Fourier transform formulas are provided and used for
quick and efficient computations. A number of useful properties of the maximal
set of kernels are derived. We also strengthen and generalize some previous
results on the classification of Gaussian kernels. Finally, a new topologically
invariant method of constructing trees is introduced.
