A contribution on real and complex convexity in several complex variables

• Autorzy: Abidi Jamel

Identyfikatory

DOI

10.7862/rf.2022.2

• Języki publikacji: EN

Abstrakty

EN

Let f, g : Cn → C be holomorphic functions. Define u(z, w) = |w − f (z)|4 + |w − g(z)|4, v(z, w) = |w − f (z)|2 + |w − g(z)|2, for (z, w) ∈ Cn × C. A comparison between the convexity of u and v is obtained under suitable conditions. Now consider four holomorphic functions φ1, φ2 : Cm → C and g1, g2 : Cn → C. We prove that F = |φ1 − g1|2 + |φ2 − g2|2 is strictly convex on Cn × Cm if and only if n = m = 1 and φ1, φ2, g1, g2 are affine functions with (φ′1g′2 − φ′2g′1)̸ = 0. Finally, it is shown that the product of four absolute values of pluriharmonic functions is plurisubharmonic if and only if the functions satisfy special conditions as well.

Słowa kluczowe

EN

holomorphic functions; convex functions; plurisubharmonic functions; inequalities; strictly; maximum principle

PL

funkcje holomorficzne; funkcje wypukłe; funkcje plurisubharmoniczne; nierówności; zasada maksimum

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2022
• Tom: Vol. 45
• Strony: 21--58
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Abidi Jamel

• Département de Mathématiques, Faculté des Sciences de Tunis, 1060 Tunis, Tunisia

• https://orcid.org/000-0002-2552-6848

Bibliografia

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