MathDB
Miklos Schweitzer 1969_6

Source:

October 15, 2008
functionintegrationcomplex analysiscomplex analysis unsolved

Problem Statement

Let x0 x_0 be a fixed real number, and let f f be a regular complex function in the half-plane ℜz>x0 \Re z>x_0 for which there exists a nonnegative function F∈L1(−∞,+∞) F \in L_1(- \infty, +\infty) satisfying ∣f(α+iβ)∣≤F(β) |f(\alpha+i\beta)| \leq F(\beta) whenever α>x0 \alpha > x_0 , −∞<β<+∞ -\infty <\beta < +\infty. Prove that ∫α−i∞α+i∞f(z)dz=0. \int_{\alpha-i \infty} ^{\alpha+i \infty} f(z)dz=0. L. Czach
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