Holomorphic Cohomological Convolution and Hadamard Product

Dubussy, Christophe; Schneiders, Jean-Pierre

doi:10.4171/PRIMS/58-1-2

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Holomorphic Cohomological Convolution and Hadamard Product

Dubussy, Christophe; Schneiders, Jean-Pierre

2022 • In Publications of the Research Institute for Mathematical Sciences, 58 (1), p. 21-48

Peer reviewed

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https://hdl.handle.net/2268/242812

DOI
10.4171/PRIMS/58-1-2

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Keywords :

Multiplicative convolution; Hadamard product; Singular homology

Abstract :

[en] In this article, we explain the link between Pohlen's extended Hadamard product and the holomorphic cohomological convolution on C^*. For this purpose, we introduce a generalized Hadamard product, which is defined even if the holomorphic functions do not vanish at infinity, as well as a notion of strongly convolvable sets.

Disciplines :

Mathematics

Author, co-author :

Dubussy, Christophe ; Université de Liège - ULiège > Département de mathématique > Analyse algébrique

Schneiders, Jean-Pierre ; Université de Liège - ULiège > Département de mathématique > Analyse algébrique

Language :

English

Title :

Holomorphic Cohomological Convolution and Hadamard Product

Alternative titles :

[fr] Convolution cohomologique holomorphe et produit d'Hadamard

Publication date :

16 February 2022

Journal title :

Publications of the Research Institute for Mathematical Sciences

ISSN :

0034-5318

eISSN :

1663-4926

Publisher :

European Mathematical Society, Zürich, Switzerland

Volume :

Issue :

Pages :

21-48

Peer reviewed :

Peer reviewed

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]

Available on ORBi :

since 07 January 2020

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Bibliography

V. Avanissian and R. Gay, Sur une transformation des fonctionnelles analytiques portables par des convexes compacts de Cd et la convolution d’Hadamard, C. R. Acad. Sci. Paris Sér. A Math. 279 (1974), 133–136. Zbl 0291.32006 MR 0352975
N. Bourbaki, Elements of mathematics: General topology. Part 1, Hermann, Paris, 1966. Zbl 0301.54001 MR 0205210
G. E. Bredon, Sheaf theory, 2nd ed., Graduate Texts in Mathematics 170, Springer, New York, 1997. Zbl 0874.55001 MR 1481706
J. Dieudonné, Éléments d’analyse. Tome III, 2nd ed., Cahiers Scientifiques Fasc. 33, Gauthier-Villars, Paris, 1980. Zbl 0208.31802 MR 0270377
C. Dubussy, Holomorphic cohomological convolution, enhanced Laplace transform and ap-plications, PhD thesis, University of Liège, Mathematics Institute, Liège, 2019.
C. Dubussy, Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems, Rend. Sem. Mat. Univ. Padova 142 (2019), 181-–209. Zbl 1450.44001 MR 4032810
M. J. Greenberg, Lectures on algebraic topology, Mathematics Lecture Note Series, W. A. Benjamin, New York, 1967. Zbl 0169.54403 MR 0215295
K. Grosse-Erdmann, On the Borel-Okada theorem and the Hadamard multiplication theo-rem, Complex Variables Theory Appl. 22 (1993), 101–112. Zbl 0794.30004 MR 1277015
A. Hatcher, Algebraic topology, Cambridge University Press, Cambridge, 2002. Zbl 1044.55001 MR 1867354
M. Kashiwara and P. Schapira, Sheaves on manifolds, Grundlehren der Mathematischen Wissenschaften 292, Springer, Berlin, 1990. Zbl 0709.18001 MR 1074006
T. Lorson, Hadamard convolution operators on spaces of holomorphic functions, PhD thesis, University of Trier, Mathematical Institute, Trier, 2014.
T. Lorson and J. Müller, Convolution operators on spaces of holomorphic functions, Studia Math. 227 (2015), 111–131. Zbl 1339.47045 MR 3397273
A. Méril, Analytic functionals with unbounded carriers and mean periodic functions, Trans. Amer. Math. Soc. 278 (1983), 115–136. Zbl 0519.46048 MR 0697064
J. Müller, The Hadamard multiplication theorem and applications in summability theory, Complex Variables Theory Appl. 18 (1992), 155–166. Zbl 0756.30002 MR 1157924
J. Müller and T. Pohlen, The Hadamard product as a universality preserving operator, Comput. Methods Funct. Theory 10 (2010), 281–289. Zbl 1205.30005 MR 2676456
J. Müller and T. Pohlen, The Hadamard product on open sets in the extended plane, Complex Anal. Oper. Theory 6 (2012), 257–274. Zbl 1294.30007 MR 2886618
T. Pohlen, The Hadamard product and universal power series, PhD thesis, University of Trier, Mathematics Institute, Trier, 2009.
J. Roe, Winding around. The winding number in topology, geometry, and analysis, Stu-dent Mathematical Library 76, American Mathematical Society, University Park, PA, 2015. Zbl 1330.55001 MR 3379904
S. L. Segal, Nine introductions in complex analysis, rev. ed., North-Holland Mathematics Studies 208, Elsevier, Amsterdam, 2008. Zbl 1233.30001 MR 0641384