Geodesic
Trigonometric convexity of the multidimensional indicator
Canadian journal of mathematics, Tome 77 (2025) no. 2, pp. 384-399

Voir la notice de l'article provenant de la source Cambridge

DOI

The notion of indicator of an analytic function, that describes the function’s growth along rays, was introduced by Phragmen and Lindelöf. Trigonometric convexity is a defining property of the indicator. For multivariate cases, an analogous property of trigonometric convexity was not known so far. We prove the property of trigonometric convexity for the indicator of multivariate analytic functions, introduced by Ivanov. The results that we obtain are sharp. Derivation of a multidimensional analogue of the inverse Fourier transform in a sector and obtaining estimates on its decay is an important step of our proof.
DOI : 10.4153/S0008414X24000014
Mots-clés : Analytic functions in several complex variables, Fourier transform, indicator function, analytic continuation, trigonometric convexity 
Mkrtchyan, Aleksandr; Vagharshakyan, Armen. Trigonometric convexity of the multidimensional indicator. Canadian journal of mathematics, Tome 77 (2025) no. 2, pp. 384-399. doi: 10.4153/S0008414X24000014
@article{10_4153_S0008414X24000014,
     author = {Mkrtchyan, Aleksandr and Vagharshakyan, Armen},
     title = {Trigonometric convexity of the multidimensional indicator},
     journal = {Canadian journal of mathematics},
     pages = {384--399},
     year = {2025},
     volume = {77},
     number = {2},
     doi = {10.4153/S0008414X24000014},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X24000014/}
}
TY  - JOUR
AU  - Mkrtchyan, Aleksandr
AU  - Vagharshakyan, Armen
TI  - Trigonometric convexity of the multidimensional indicator
JO  - Canadian journal of mathematics
PY  - 2025
SP  - 384
EP  - 399
VL  - 77
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X24000014/
DO  - 10.4153/S0008414X24000014
ID  - 10_4153_S0008414X24000014
ER  - 
%0 Journal Article
%A Mkrtchyan, Aleksandr
%A Vagharshakyan, Armen
%T Trigonometric convexity of the multidimensional indicator
%J Canadian journal of mathematics
%D 2025
%P 384-399
%V 77
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008414X24000014/
%R 10.4153/S0008414X24000014
%F 10_4153_S0008414X24000014

Cité par Sources :