Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 449-457

EXAMPLES OF DE BRANGES–ROVNYAK SPACES GENERATED BY NONEXTREME FUNCTIONS

Bartosz Lanucha and Maria T. Nowak

Maria Curie-Sklodowska University, Institute of Mathematics
pl. M. Curie-Sklodowskiej 1, 20-031 Lublin, Poland; bartosz.lanucha 'at' poczta.umcs.lublin.pl

Maria Curie-Sklodowska University, Institute of Mathematics
pl. M. Curie-Sklodowskiej 1, 20-031 Lublin, Poland; mt.nowak 'at' poczta.umcs.lublin.pl

Abstract. We describe de Branges–Rovnyak spaces H(b_α), α > 0, where the function b_α is not extreme in the unit ball of H^∞ on the unit disk D, defined by the equality b_α(z)/a_α(z) = (1 – z)^-α, z ∈ D, where a_α is the outer function such that a_α(0) > 0 and |a_α|² + |b_α|² = 1 a.e. on ∂D.

2010 Mathematics Subject Classification: Primary 47B32, 30H10, 30H15.

Key words: Hardy space, de Branges–Rovnyak space, Smirnov class, rigid function.

Reference to this article: B. Lanucha and M. T. Nowak: Examples of de Branges–Rovnyak spaces generated by nonextreme functions. Ann. Acad. Sci. Fenn. Math. 44 (2019), 449-457.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4427