Geodesic
Locally explicit fundamental principle for homogeneous convolution equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 466-474.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the present paper a locally explicit version of Ehrenpreis's Fundamental Principle for a system of homogeneous convolution equations $\check{f}\ast \mu_j=0$, $j=1,\dots, m $, $f\in\mathcal{E}(\mathbb{R}^n)$, $\mu_j\in\mathcal{E}^{\prime}(\mathbb{R}^n)$, is derived, when the Fourier Transforms $\hat{\mu}_j$, $j=1,\dots, m$ are slowly decreasing entire functions that form a complete intersection in $\mathbb{C}^n$.
Keywords: fundamental principle
Mots-clés : division formula. 
@article{JSFU_2019_12_4_a8,
     author = {Alekos Vidras},
     title = {Locally explicit fundamental principle for homogeneous convolution equations},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {466--474},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_4_a8/}
}
TY  - JOUR
AU  - Alekos Vidras
TI  - Locally explicit fundamental principle for homogeneous convolution equations
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2019
SP  - 466
EP  - 474
VL  - 12
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2019_12_4_a8/
LA  - en
ID  - JSFU_2019_12_4_a8
ER  - 
%0 Journal Article
%A Alekos Vidras
%T Locally explicit fundamental principle for homogeneous convolution equations
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2019
%P 466-474
%V 12
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2019_12_4_a8/
%G en
%F JSFU_2019_12_4_a8
Alekos Vidras. Locally explicit fundamental principle for homogeneous convolution equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 466-474. http://geodesic.mathdoc.fr/item/JSFU_2019_12_4_a8/

[1] L.A. Aizenberg, A.P. Yuzhakov, Integral Representations in Multidimensional Complex Analysis, Transl. AMS, 58, 1980 | MR

[2] M. Andersson, M. Passare, “A shortcut to weighted representation formulas for holomorphic functions”, Ark. Mat., 26:1 (1988), 1–12 | DOI | MR | Zbl

[3] C.A. Berenstein, B.A. Taylor, “Interpolation problems in Cn with applications to harmonic analysis”, J. Analyse Math., 38 (1980), 188–254 | DOI | MR | Zbl

[4] C.A. Berenstein, R. Gay, Complex Analysis and Special Topics in Harmonic Analysis, Springer-Verlag, 1991 | MR

[5] C.A. Berenstein, R. Gay, A. Vidras, A. Yger, Residue currents and Bézout identities, Progress in Mathematics, 114, Birkhäuser, 1993 | MR

[6] C.A. Berenstein, A. Yger, “About Ehrenpreis' Fundamental Principle”, Geom. and alg. aspects in several complex variables, eds. C.A. Berenstein, D.C. Struppa, Editel, Rende, 1991, 47–61 | MR | Zbl

[7] B. Berndtsson, M. Andersson, “Henkin-Ramirez formulas with weight factors”, Ann. Inst. Fourier (Grenoble), 32:3 (1982), 91–110 | DOI | MR | Zbl

[8] B. Berndtsson, M. Passare, “Integral formulas and an explicit version of the fundamental principle”, J. Funct. Anal., 84:2 (1989), 358–372 | DOI | MR | Zbl

[9] L. Ehrenpreis, Fourier Analysis in Several Complex variables, Wiley, New York, 1970 | MR | Zbl

[10] S. Hansen, “Localizable analytically uniform spaces and the fundamental principle”, Tran. of AMS, 264:1 (1981), 235–250 | DOI | MR | Zbl