On semiconvexity properties of rotationally invariant functions in two dimensions

Miroslav Šilhavý

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 3, page 559-571
  • ISSN: 0011-4642

Abstract

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Let f be a function defined on the set 𝐌 2 × 2 of all 2 by 2 matrices that is invariant with respect to left and right multiplications of its argument by proper orthogonal matrices. The function f can be represented as a function f ˜ of the signed singular values of its matrix argument. The paper expresses the ordinary convexity, polyconvexity, and rank 1 convexity of f in terms of its representation f ˜ .

How to cite

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Šilhavý, Miroslav. "On semiconvexity properties of rotationally invariant functions in two dimensions." Czechoslovak Mathematical Journal 54.3 (2004): 559-571. <http://eudml.org/doc/30882>.

@article{Šilhavý2004,
abstract = {Let $f$ be a function defined on the set $\{\mathbf \{M\}\}^\{2\times 2\}$ of all $2$ by $2$ matrices that is invariant with respect to left and right multiplications of its argument by proper orthogonal matrices. The function $f$ can be represented as a function $\tilde\{f\}$ of the signed singular values of its matrix argument. The paper expresses the ordinary convexity, polyconvexity, and rank 1 convexity of $f$ in terms of its representation $\tilde\{f\}.$},
author = {Šilhavý, Miroslav},
journal = {Czechoslovak Mathematical Journal},
keywords = {semiconvexity; rank 1 convexity; polyconvexity; convexity; rotational invariance; semiconvexity; rank 1 convexity; polyconvexity; convexity; rotational invariance},
language = {eng},
number = {3},
pages = {559-571},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On semiconvexity properties of rotationally invariant functions in two dimensions},
url = {http://eudml.org/doc/30882},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Šilhavý, Miroslav
TI - On semiconvexity properties of rotationally invariant functions in two dimensions
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 3
SP - 559
EP - 571
AB - Let $f$ be a function defined on the set ${\mathbf {M}}^{2\times 2}$ of all $2$ by $2$ matrices that is invariant with respect to left and right multiplications of its argument by proper orthogonal matrices. The function $f$ can be represented as a function $\tilde{f}$ of the signed singular values of its matrix argument. The paper expresses the ordinary convexity, polyconvexity, and rank 1 convexity of $f$ in terms of its representation $\tilde{f}.$
LA - eng
KW - semiconvexity; rank 1 convexity; polyconvexity; convexity; rotational invariance; semiconvexity; rank 1 convexity; polyconvexity; convexity; rotational invariance
UR - http://eudml.org/doc/30882
ER -

References

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