[Critères de surjectivité pour des opérateurs de convolution dans ]
Le but de cet article est d'établir des critères de surjectivité pour des opérateurs de convolution, opérant de dans (Ω et K étant, respectivement, un domaine convexe borné et un compact convexe dans ). Ils seront obtenus en les reliant au problème de division. Une représentation explicite des solutions des équations de convolution correspondantes sera également donnée sous forme de série de Dirichlet.
The goal of this Note is to prove criteria for surjectivity of convolution operators acting from into (Ω and K being a bounded convex domain and a convex compact set in , respectively). This is obtained in a connection with the division problem. The explicit representation of solutions of the corresponding convolution equations in a form of Dirichlet series is also given.
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Alexander V. Abanin 1 ; Ryuichi Ishimura 2 ; Le Hai Khoi 3
@article{CRMATH_2010__348_5-6_253_0, author = {Alexander V. Abanin and Ryuichi Ishimura and Le Hai Khoi}, title = {Surjectivity criteria for convolution operators in $ {A}^{-\infty }$}, journal = {Comptes Rendus. Math\'ematique}, pages = {253--256}, publisher = {Elsevier}, volume = {348}, number = {5-6}, year = {2010}, doi = {10.1016/j.crma.2010.01.015}, language = {en}, }
TY - JOUR AU - Alexander V. Abanin AU - Ryuichi Ishimura AU - Le Hai Khoi TI - Surjectivity criteria for convolution operators in $ {A}^{-\infty }$ JO - Comptes Rendus. Mathématique PY - 2010 SP - 253 EP - 256 VL - 348 IS - 5-6 PB - Elsevier DO - 10.1016/j.crma.2010.01.015 LA - en ID - CRMATH_2010__348_5-6_253_0 ER -
Alexander V. Abanin; Ryuichi Ishimura; Le Hai Khoi. Surjectivity criteria for convolution operators in $ {A}^{-\infty }$. Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 253-256. doi : 10.1016/j.crma.2010.01.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.01.015/
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