Clebsch-Gordan problem and coefficients for the three-dimensional Lorentz group in a continuous basis. I

We have described a new approach to the Clebsch‐Gordan problem for the unitary representations of the three‐dimensional Lorentz group. We relate the various types of Clebsch‐Gordan series to problems in the representation theory of four‐dimensional orthogonal and pseudo‐orthogonal groups, and thereby achieve a new and better understanding of the structures of the series. At the same time, the Clebsch‐Gordan coefficients in a continuous basis are calculated. In this, the first of four papers, the case $D^{+}{\mathrm{\otimes D}}^{+}$ is worked out in detail.