Reproducing Subgroups of \(Sp(2,\mathbb{R})\). Part I: Algebraic Classification

We classify the connected Lie subgroups of the symplectic group \(Sp(2,{\mathbb{R}})\) whose elements are matrices in block lower triangular form. The classification is up to conjugation within \(Sp(2,{\mathbb{R}})\). Their study is motivated by the need of a unified approach to continuous 2D signal analyses, as those provided by wavelets and shearlets.