The Corona Property in Nevanlinna quotient algebras and Interpolating sequences

Autor: Xavier Massaneda, Pascal J. Thomas, Artur Nicolau
Přispěvatelé: Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT), Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona (UB), Departament de Matemàtiques [Barcelona] (UAB), Universitat Autònoma de Barcelona (UAB), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Fédérale Toulouse Midi-Pyrénées
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Pure mathematics
Class (set theory)
Property (philosophy)
Funcions de variables complexes
Quotient algebra
[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA]
01 natural sciences
Functions of complex variables
0103 physical sciences
Classical Analysis and ODEs (math.CA)
FOS: Mathematics
Complex Variables (math.CV)
0101 mathematics
Quotient
Mathematics
Nevanlinna theory
Mathematics - Complex Variables
Mathematics::Complex Variables
Geometric function theory
010102 general mathematics
[MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV]
Function (mathematics)
Teoria de Nevanlinna
16. Peace & justice
Unit disk
Mathematics - Classical Analysis and ODEs
Bounded function
30H15
30H80
30J10
Teoria geomètrica de funcions
010307 mathematical physics
Analysis
Analytic function
Zdroj: Journal of Functional Analysis
Journal of Functional Analysis, 2019, 276, pp.2636-2661. ⟨10.1016/j.jfa.2018.08.001⟩
Journal of Functional Analysis, Elsevier, 2019, 276, pp.2636-2661. ⟨10.1016/j.jfa.2018.08.001⟩
ISSN: 0022-1236
1096-0783
DOI: 10.1016/j.jfa.2018.08.001⟩
Popis: Let $I$ be an inner function in the unit disk $\mathbb D$ and let $\mathcal N$ denote the Nevanlinna class. We prove that under natural assumptions, Bezout equations in the quotient algebra $\mathcal N/I\mathcal N$ can be solved if and only if the zeros of $I$ form a finite union of Nevanlinna interpolating sequences. This is in contrast with the situation in the algebra of bounded analytic functions, where being a finite union of interpolating sequences is a sufficient but not necessary condition. An analogous result in the Smirnov class is proved as well as several equivalent descriptions of Blaschke products whose zeros form a finite union of interpolating sequences in the Nevanlinna class.
22 pages
Databáze: OpenAIRE
Externí odkaz: