Open Access
2010/2011 Convexity in Real Analysis
Steven G. Krantz
Real Anal. Exchange 36(1): 1-28 (2010/2011).


We treat the classical notion of convexity in the context of hard real analysis. Definitions of the concept are given in terms of defining functions and quadratic forms, and characterizations are provided of different concrete notions of convexity. This analytic notion of convexity is related to more classical geometric ideas. Applications are given both to analysis and geometry.


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Steven G. Krantz. "Convexity in Real Analysis." Real Anal. Exchange 36 (1) 1 - 28, 2010/2011.


Published: 2010/2011
First available in Project Euclid: 14 March 2011

zbMATH: 1246.26010
MathSciNet: MR3016400

Primary: 26B25
Secondary: 52A05

Keywords: Convex domain , convex function , Finite order , Hessian , quadratic form

Rights: Copyright © 2010 Michigan State University Press

Vol.36 • No. 1 • 2010/2011
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