Representing systems of exponential functions in spaces of holomorphic functions with given growth near boundary
Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 4, pp. 5-9
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We consider $(LB)$ spaces of functions which are holomorphic in a convex domain and have a finite type with respect to an order near its boundary. Using Laplace transformation, we give a description of their duals. Then we characterize mimimal absolutely representing systems of exponential functions in these spaces and prove that they always exist.
@article{VMJ_2012_14_4_a0,
author = {A. V. Abanin and V. A. Varziev},
title = {Representing systems of exponential functions in spaces of holomorphic functions with given growth near boundary},
journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
pages = {5--9},
publisher = {mathdoc},
volume = {14},
number = {4},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a0/}
}
TY - JOUR AU - A. V. Abanin AU - V. A. Varziev TI - Representing systems of exponential functions in spaces of holomorphic functions with given growth near boundary JO - Vladikavkazskij matematičeskij žurnal PY - 2012 SP - 5 EP - 9 VL - 14 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a0/ LA - ru ID - VMJ_2012_14_4_a0 ER -
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A. V. Abanin; V. A. Varziev. Representing systems of exponential functions in spaces of holomorphic functions with given growth near boundary. Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 4, pp. 5-9. http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a0/