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Sampling measures, muckenhoupt hamiltonians, and triangular factorization. / Bessonov, Roman.
в: International Mathematics Research Notices, Том 2018, № 12, 01.06.2018, стр. 3744-3768.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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 -
ID: 36320737