Muckenhoupt Hamiltonians, triangular factorization, and Krein orthogonal entire functions
| Title: | Muckenhoupt Hamiltonians, triangular factorization, and Krein orthogonal entire functions |
|---|---|
| Authors: | Bessonov, Roman |
| Source: | IWOTA 2016 |
| Publisher Information: | Washington University Open Scholarship |
| Publication Year: | 2016 |
| Collection: | Washington University St. Louis: Open Scholarship |
| Description: | According to classical results by M. G. Krein and L. de Branges, for every positive measure $\mu$ on the real line $\mathbb{R}$ such that $\int_{\mathbb{R}} \frac{d\mu(t)}{1 + t^2} < \infty$ there exists a Hamiltonian $H$ such that $\mu$ is the spectral measure for the corresponding canonical Hamiltonian system $JX' = z HX$. In the case where $\mu$ is an even measure from Steklov class on $\mathbb{R}$, we show that the Hamiltonian $H$ normalized by $\det H = 1$ belongs to the classical Muckenhoupt class $A_2$. Applications of this result to triangular factorizations of Wiener-Hopf operators and Krein orthogonal entire functions will be also discussed. |
| Document Type: | text |
| File Description: | application/pdf |
| Language: | unknown |
| Relation: | https://openscholarship.wustl.edu/iwota2016/special/OTPDE/3; https://openscholarship.wustl.edu/context/iwota2016/article/1110/viewcontent/everything_11.pdf |
| Availability: | https://openscholarship.wustl.edu/iwota2016/special/OTPDE/3; https://openscholarship.wustl.edu/context/iwota2016/article/1110/viewcontent/everything_11.pdf |
| Accession Number: | edsbas.BA7AE74 |
| Database: | BASE |