On the approximation of analytic functions in a strip
1985 ◽
Vol 97
(3)
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pp. 381-384
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Keyword(s):
The Real
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1. Letand 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 errorwhere ∥·∥∞ 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
1984 ◽
Vol 27
(4)
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pp. 463-471
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1958 ◽
Vol 10
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pp. 122-126
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Keyword(s):
1922 ◽
Vol 41
◽
pp. 82-93
1975 ◽
Vol 20
(1)
◽
pp. 46-53