Geodesic
Principal submodules in the module of entire functions, which is dual to the Schwartz space, and weak spectral synthesis in the Schwartz space
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 142 (2017), pp. 14-27.

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We obtain a sufficient condition of the weak localizability of a principal submodule in the module of entire functions of exponential type and polynomial growth on the real line. Applications to the problem of the (weak) spectral synthesis in the Schwartz space $C^{\infty}(a;b)$ are discussed.
Keywords: entire functions, subharmonic functions, local descripstion of submodules, spectral synthesis.
Mots-clés : Fourier–Laplace transform, invariant spaces 
@article{INTO_2017_142_a1,
     author = {N. F. Abuzyarova},
     title = {Principal submodules in the module of entire functions, which is dual to the {Schwartz} space, and weak spectral synthesis in the {Schwartz} space},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {14--27},
     publisher = {mathdoc},
     volume = {142},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_142_a1/}
}
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N. F. Abuzyarova. Principal submodules in the module of entire functions, which is dual to the Schwartz space, and weak spectral synthesis in the Schwartz space. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 142 (2017), pp. 14-27. http://geodesic.mathdoc.fr/item/INTO_2017_142_a1/