TY - JOUR

T1 - Sampling measures, muckenhoupt hamiltonians, and triangular factorization

AU - Bessonov, Roman

PY - 2018/6/1

Y1 - 2018/6/1

N2 - Let μ be an even measure on the real line R such that c1 R |f |2 dx R |f |2 dμ c2 R |f |2 dx for all functions f in the Paley–Wiener space PWa. We prove that μ is the spectral measure for the unique Hamiltonian H = w 0 w 01 on [0, a] generated by a weight w from the Muckenhoupt class A2[0, a]. As a consequence of this result, we construct Krein’s orthogonal entire functions with respect to μ and prove that every positive, bounded, invertible Wiener–Hopf operator on [0, a] with real symbol admits triangular factorization.

AB - Let μ be an even measure on the real line R such that c1 R |f |2 dx R |f |2 dμ c2 R |f |2 dx for all functions f in the Paley–Wiener space PWa. We prove that μ is the spectral measure for the unique Hamiltonian H = w 0 w 01 on [0, a] generated by a weight w from the Muckenhoupt class A2[0, a]. As a consequence of this result, we construct Krein’s orthogonal entire functions with respect to μ and prove that every positive, bounded, invertible Wiener–Hopf operator on [0, a] with real symbol admits triangular factorization.

KW - TRUNCATED TOEPLITZ-OPERATORS

UR - http://www.scopus.com/inward/record.url?scp=85050695607&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnx019

DO - 10.1093/imrn/rnx019

M3 - Article

AN - SCOPUS:85050695607

VL - 2018

SP - 3744

EP - 3768

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 12

ER -