Linear canonical Stockwell transform and the associated multiresolution analysis

In this article, we propose a new class of transform called linear canonical Stockwell transform (LCST) and obtain its basic properties along with the inner product relation and reconstruction formula. We characterize the range of the transform and show that its range is the reproducing kernel Hilbert space. We also develop a multiresolution analysis (MRA) associated with the proposed transform together with the construction of the orthonormal basis for L2(Double-struck capital R)$$ {L} circumflex 2\left(\mathrm{\mathbb{R}}\right) $$.