I have introduced some factorization for the infinite Hilbert Operator based on the Cesaro, generalized Cesaro and Gamma matrices in the following papers:

1-H. Roopaei, Factorization of Cesàro and Hilbert matrices based on generalized Cesàro

matrix, Linear Multilinear Algebra, 68 (1) (2020), 193-204.

2-H. Roopaei, Factorization of the Hilbert matrix based on Cesàro and Gamma matrices,

Results Math., 75 (1) 3, 2020. DOI: 10.1007/s00025-019-1129-1.

Now, my questions are:

1-Is there any other factorization for the Hilbert matrix based on the Hausdorff operators? and in especial case of Hausdorff classes, based on Euler or Holder operators?

2- As I know the infinite Hilbert operator is used in Cryptography and Image processing. Is there any mathematicians in this group who can introduce some good references?