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Reducibility for a Class of Analytic Multipliers on the Dirichlet Space
- Source :
- Complex Analysis and Operator Theory. 12:1781-1790
- Publication Year :
- 2017
- Publisher :
- Springer Science and Business Media LLC, 2017.
-
Abstract
- It is proved that if \(\phi \) is a finite Blaschke product with four zeros, then \(M_\phi \) is reducible on the Dirichlet space with norm \(\Vert \ \Vert \) if and only if \(\phi =\phi _1\circ \phi _2\), where \(\phi _1, \phi _2\) are Blaschke products and \(\phi _2\) is equivalent to \(z^2\). Also, the same reducibility of \(M_\phi \) with finite Blaschke product \(\phi \) on the Dirichlet space under the equivalent norms \(\Vert \ \Vert _1\) and \(\Vert \ \Vert _0\) is given.
- Subjects :
- Mathematics::Functional Analysis
Applied Mathematics
Blaschke product
High Energy Physics::Phenomenology
010102 general mathematics
Mathematical analysis
Mathematics::Analysis of PDEs
Mathematics::Spectral Theory
Operator theory
Computer Science::Numerical Analysis
01 natural sciences
Dirichlet space
010101 applied mathematics
Combinatorics
Computational Mathematics
symbols.namesake
Computational Theory and Mathematics
symbols
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 16618262 and 16618254
- Volume :
- 12
- Database :
- OpenAIRE
- Journal :
- Complex Analysis and Operator Theory
- Accession number :
- edsair.doi...........798cdd6588e545578d2a7cf639179f84