Muckenhoupt Hamiltonians, triangular factorization, and Krein orthogonal entire functions
نویسنده
چکیده
According to classical results by M. G. Krein and L. de Branges, for every positive measure μ on the real line R such that ∫ R dμ(t) 1+t2 <∞ there exists a Hamiltonian H such that μ is the spectral measure for the corresponding canonical Hamiltonian system JX ′ = zHX. In the case where μ is an even measure from Steklov class on R, we show that the Hamiltonian H normalized by detH = 1 belongs to the classical Muckenhoupt class A2. Applications of this result to triangular factorizations of Wiener-Hopf operators and Krein orthogonal entire functions will be also discussed.
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