Work

Efficient computation for the eigenvalues and eigenfunctions of two-dimensional non-separable linear canonical transform

Year: 2025

Type: article

Abstract: The parameter matrix of the two-dimensional non-separable linear canonical transform (2D-NSLCT) determines its specific form and properties. Certain forms of the 2D-NSLCT are consistent with well-known transforms, such as two-dimensional non-separable fractional Fourier transform (2D-NSFrFT), Fresnel transform, and other related transforms. Based on the analysis of the eigenvalues and eigenfunctions of these special transforms, this paper proposes an efficient method for computing the eigenvalues and eigenfunctions of the 2D-NSLCT. Specifically, based on the properties of similar matrices, if the parameter matrix of the 2D-NSLCT is similar to that of a special transform (e.g., 2D-NSFrFT or other transforms), then the eigenvalues of the 2D-NSLCT are identical to those of the special transform. Moreover, the eigenfunctions of the 2D-NSLCT can be computed using the known eigenfunctions of this special transform based on the additivity of the 2D-NSLCT. The detailed derivation is presented in this paper, and some applications of the 2D-NSLCT’s eigenfunction are also discussed. • This paper mainly discusses how to compute the eigenfunctions of the 2D-NSLCT. • The computational method leverages the similarity relationships among parameter matrices. • The detailed calculation process is presented, and some applications are also discussed.

Source: Results in Applied Mathematics

DOI: 10.1016/j.rinam.2025.100645

Authors: Yuru Tian, Feng Zhang

Institution: Beijing Institute of Technology

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,770

Funder: National Natural Science Foundation of China