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Improved Heinz inequalities via the Jensen functional

Mario Krnić, Josip Pečarić (2013)

Open Mathematics

By virtue of convexity of Heinz means, in this paper we derive several refinements of Heinz norm inequalities with the help of the Jensen functional and its properties. In addition, we discuss another approach to Heinz operator means which is more convenient for obtaining the corresponding operator inequalities for positive invertible operators.

L 2 -estimates for the d -equation and Witten’s proof of the Morse inequalities

Bo Berndtsson (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

This is an introduction to Witten’s analytic proof of the Morse inequalities. The text is directed primarily to readers whose main interest is in complex analysis, and the similarities to Hörmander’s L 2 -estimates for the ¯ -equation is used as motivation. We also use the method to prove L 2 -estimates for the d -equation with a weight e - t φ where φ is a nondegenerate Morse function.

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