Geodesic
Representing systems of exponentials in projective limits of weigth subspaces of $A^\infty (D)$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2019), pp. 29-41

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We introduce a normed space of functions holomorphic in a bounded convex domain which are infinitely differentiable up to the boundary and have certain estimates of all derivatives given by a convex sequence of positive numbers. We consider its largest linear subspace that is invariant with respect to the operator of differentiation, in which the natural topology of the projective limit is introduced. We prove the duality of this subspace and a certain space of entire functions. Based on this, we construct the representing system of exponentials in it.
Keywords: analytic function, weighted space, locally convex space, sufficient set, representing system of exponentials. 
@article{IVM_2019_1_a2,
     author = {K. P. Isaev},
     title = {Representing systems of exponentials in projective limits of weigth subspaces of $A^\infty (D)$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {29--41},
     publisher = {mathdoc},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_1_a2/}
}
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K. P. Isaev. Representing systems of exponentials in projective limits of weigth subspaces of $A^\infty (D)$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2019), pp. 29-41. http://geodesic.mathdoc.fr/item/IVM_2019_1_a2/