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MacLane functions with prescribed zeros and interpolation properties
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Markus Nieß
Published/Copyright:
September 25, 2009
An entire function ϕ is called universal in the sense of MacLane (for short MacLane function) if for any preassigned entire function f a suitable sequence ϕ(nk) of derivatives of ϕ converges to f locally uniformly in the whole plane.
It is shown that for every appropriate choice of designated zeros in ℂ, there exists a MacLane function having zeros exactly in these points, of preassigned order. Moreover, there exist MacLane functions satisfying an interpolation problem in addition.
Keywords: Spaces of entire functions; universality; approximation by derivatives; zeros; interpolation
Received: 2006-11-18
Published Online: 2009-9-25
Published in Print: 2007-10-1
© Oldenbourg Wissenschaftsverlag
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Keywords for this article
Spaces of entire functions;
universality;
approximation by derivatives;
zeros;
interpolation
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
