Metamorphism as a covariant transform for the SSR group
arXiv:2301.05879 · doi:10.1007/s40590-023-00505-3
Abstract
Metamorphism is a recently introduced integral transform, which is useful in solving partial differential equations. Basic properties of metamorphism can be verified by direct calculations. In this paper we present metamorphism as a sort of covariant transform and derive its most important features in this way. Our main result is a characterisation of metamorphism's image space. Reading this paper does not require advanced knowledge of group representations or theory of covariant transform.
arXiv comment15 pp. AMS-LaTeX; v2: minor improvements; v3: a couple of references is added
References in corpus (12)
- Erlangen Programme at Large: An Overview
- Erlangen Program at Large-2.5: Induced Representations and Hypercomplex Numbers
- p-Mechanics as a Physical Theory. An Introduction
- Geometric Dynamics of a Harmonic Oscillator, Arbitrary Minimal Uncertainty States and the Smallest Step 3 Nilpotent Lie Group
- Erlangen Programme at Large 3.1: Hypercomplex Representations of the Heisenberg Group and Mechanics
- Symmetry, Geometry, and Quantization with Hypercomplex Numbers
- Uncertainty and Analyticity
- Covariant Transform
- Solving the Schrodinger Equation by Reduction to a First-order Differential Operator through a Coherent States Transform
- Cross-Toeplitz Operators on the Fock--Segal--Bargmann Spaces and Two-Sided Convolutions on the Heisenberg Group
- Tuning Co- and Contra-Variant Transforms: the Heisenberg Group Illustration
- Metamorphism -- an Integral Transform Reducing the Order of a Differential Equation