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On the approximation of analytic functions in a strip

Published online by Cambridge University Press:  24 October 2008

Dieter Klusch
Dieter Klusch
Affiliation:
Tanneck 7, D-2370 Rendsburg, West Germany
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Extract

1. Let

and denote by Aδ the class of functions f analytic in the strip Sδ = {z = x + iy| |y| < δ}, real on the real axis, and satisfying |Ref(z)| ≤ 1,z∊Sδ. Then N.I. Achieser ([1], pp. 214–219; [8], pp. 137–8, 149) proved that each f∊Aδ can be uniformly approximated on the whole real axis by an entire function fc of exponential type at most c with an error

where ∥·∥∞ is the sup norm on ℝ. Furthermore ([7], pp. 196–201), if f∊Aδ is 2π-periodic, then the uniform approximation Ẽn (Aδ) of the class Aδ by trigonometric polynomials of degree at most n is given by

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 3 , May 1985 , pp. 381 - 384
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

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