Integral Valued Entire Functions

Carlos A. Berenstein and Roger Gay
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Carlos A. Berenstein: University of Maryland, Mathematics Department and Institute for Systems Research
Roger Gay: Université de Bordeaux I, Centre de Recherche en Mathématiques

Chapter Chapter 4 in Complex Analysis and Special Topics in Harmonic Analysis, 1995, pp 260-298 from Springer

Abstract: Abstract In this section we study a transform of analytic functionals akin to the Cauchy transform considered in Chapter 1. This transform will allow us to obtain rather easily those properties of entire functions of exponential type that can be derived from their behavior on sequences of the form n ≥ n0, n ∈ ℤ. It also provides an elementary method to study the analytic continuation of power series of the form Σ≥0 f (n)t n , where f is an entire function of exponential type. The main references for this section are [Bo], [Av 1], [Av2], [AG1], [AG2], [AG3].

Date: 1995
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DOI: 10.1007/978-1-4613-8445-8_4

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