THE EXTREME POINTS OF A CLASS OF ANALYTIC FUNCTIONS WITH POSITIVE REAL PART AND A PRESCRIBED SET OF VALUES

doi:10.1016/S0252-9602(12)60150-7

Abstract

Abstract:

Let ζ = (0, z₁, z₂, · · · , z_n) with |z_j| < 1 for 1 ≤ j ≤ n, ! = (1, w₁, w₂, · · · , w_n), and P(ζ, ω) denote the set of functions p(z) that are analytic in D = {z : |z| < 1} and satisfy Rep(z) > 0 (|z| < 1), p(0) = 1, p(z_j) = w_j, j = 1, 2, · · · , n. In this article we investigate the extreme points of P(ζ, ω).

Key words: extreme point, positive real part, Blaschke product

CLC Number:

30C45

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PENG Zhi-Gang. THE EXTREME POINTS OF A CLASS OF ANALYTIC FUNCTIONS WITH POSITIVE REAL PART AND A PRESCRIBED SET OF VALUES[J].Acta mathematica scientia,Series B, 2012, 32(5): 1929-1936.

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References

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