Properties of the Level Sets of Some Products of Functions

Abstract

We are interested about pairs

(f,g)

of

C^2

-smooth functions

f,g:\mathbb{R}^n\longrightarrow\mathbb{R}

with bounded

{\rm Hess}^+

complements such that their product preserves this property as well. Recall that

{\rm Hess}^+(f)

stands for the set of all points

p\in\mathbb{R}^n

such that the Hessian matrix

H_p(f)

of the

C^2

-smooth function

f\colon \mathbb{R}^n\longrightarrow\mathbb{R}

is positive definite. In this paper we consider two pairs of real-valued functions with empty

{\rm Hess}^+

complements whose products happen to have bounded

{\rm Hess}^+

complements.

Contact details are reproduced from the original publication and may be historical.

Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania

Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania

47H05; 47H99

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Published by Heldermann Verlag, 2023. Rights now held by Banach Press LLC.