Abstract
In this chapter we consider certain properties of entire functions of exponential type, bounded on the real space ℝ n = ℝ. We see that they are very analogous to the corresponding properties of trigonometric polynomials. While trigonometric polynomials are a good means of approximation of periodic functions, entire functions of exponential type may serve as a means of approximation1 of nonperiodic functions, given on n-dimensional space. Perhaps the reader inexperienced in these questions ought to start this chapter by reading 3.1.1, where we give in addition general information on the theory of multiple power series.
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© 1975 Springer-Verlag Berlin Heidelberg
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Nikol’skii, S.M. (1975). Entire Functions of Exponential Type, Bounded on ℝ. In: Approximation of Functions of Several Variables and Imbedding Theorems. Die Grundlehren der mathematischen Wissenschaften, vol 205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65711-5_4
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DOI: https://doi.org/10.1007/978-3-642-65711-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65713-9
Online ISBN: 978-3-642-65711-5
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