## Operator theory, singular integral equations, and PDEs

#### Location

Cupples I Room 115

#### Start Date

7-18-2016 3:30 PM

#### End Date

18-7-2016 3:50 PM

#### 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.

#### Share

COinS

Jul 18th, 3:30 PM Jul 18th, 3:50 PM

Muckenhoupt Hamiltonians, triangular factorization, and Krein orthogonal entire functions

Cupples I Room 115

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.