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On some representation formulas involving moduli of Blaschke products
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Alan Gluchoff
Published/Copyright:
September 25, 2009
Starting from an integral formula in harmonic analysis, we derive some representation formulas for (1–|B(z)|2)/(1–|z|2) in terms of the zeros of the underlying interpolating Blaschke product B. We use our formula to show that for every interpolating Blaschke product B there exists another interpolating Blaschke product C, with zeros distinct from those of B, such that C is orthogonal to B in H2.
Received: 2006-8-3
Published Online: 2009-9-25
Published in Print: 2007-10-1
© Oldenbourg Wissenschaftsverlag
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Articles in the same Issue
- In memoriam Gerald Schmieder
- A general cross theorem with singularities
- Bounded pointwise approximation on open Riemann surfaces
- Generalized Fourier expansion in kernels of convolution operators on Fourier hyperfunctions
- Stein's extension operator for sets with Lipγ-boundary
- On some representation formulas involving moduli of Blaschke products
- Universal (pluri)subharmonic functions
- Uniform approximation on the real axes by functions harmonic in a stripe and having optimal growth
- Univalence of a complex linear combination of two extremal parallel slit mappings
- Lacunary (R, p, M)-summability
- MacLane functions with prescribed zeros and interpolation properties
- Reasoning and proof in the mathematics classroom
