On recurrence coefficients of Steklov measures

• Autores: Roman V. Bessonov
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 69, Fasc. 2, 2018, págs. 237-248
• Idioma: inglés
• DOI: 10.1007/s13348-017-0203-9
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• Resumen

  • A measure ? on the unit circle ? belongs to Steklov class if its density w with respect to the Lebesgue measure on ? is strictly positive: essinf??>0 . Let ? , ?−1 be measures on the unit circle ? with real recurrence coefficients {??} , {−??} , correspondingly. If ?∈ and ?−1∈ , then partial sums ??=?0+…+?? satisfy the discrete Muckenhoupt condition sup?>ℓ⩾0(1?−ℓ∑?−1?=ℓ?2??)(1?−ℓ∑?−1?=ℓ?−2??)<∞ .