Preservation of classes of entire functions defined in terms of growth restrictions along the real axis under perturbations of their zero sets. (English. Russian original) Zbl 1501.30009
St. Petersbg. Math. J. 33, No. 4, 585-606 (2022); translation from Algebra Anal. 33, No. 4, 1-31 (2021).
Summary: Four special subsets of the Schwartz algebra are defined (this algebra consists of all entire functions of exponential type and of polynomial growth on the real axis). Perturbations of the zero sets for functions belonging to each of these subsets are studied. It is shown that the boundedness of the real part of the perturbing sequence is a sufficient and, generally speaking, unimprovable condition for preservation the subset from which the function in question is taken. An application of these results to spectral synthesis problems for differentiation-invariant subspaces of the Schwartz class on an interval of the real line is considered.
MSC:
| 30D15 | Special classes of entire functions of one complex variable and growth estimates |
| 30C15 | Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) |
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