Abstract:
Let $f$ be a solution of the equation
\begin{equation*}
S*f=0
\end{equation*}
with characteristic function $\varphi$, $D_f$ is the trace which is left by the associated diagram $D$ of the function $\varphi$ under a continuous translational displacement as a geometric figure on the Riemann surface of the function $f$. We show that $D_f$ is a one-sheeted simply connected region; the function $f$ can be uniformly approximated inside $D_f$ by linear combinations of elementary solutions. This result is a corollary of a more general theorem on the extension of spectral synthesis which is proved in this paper.
Figures: 2.
Bibliography: 14 titles.
Citation:
I. F. Krasichkov-Ternovskii, “Invariant subspaces of analytic functions. III. On the extension of spectral synthesis”, Math. USSR-Sb., 17:3 (1972), 327–348
This publication is cited in the following 43 articles:
N. F. Abuzyarova, Z. Yu. Fazullin, “Invariant subspaces in non-quasianalytic spaces of $\Omega$-ultradifferentiable functions on an interval”, Eurasian Math. J., 15:3 (2024), 9–24
N. F. Abuzyarova, “Invariantnye podprostranstva v nekvazianaliticheskikh prostranstvakh $\Omega$-ultradifferentsiruemykh funktsii na intervale”, Izv. vuzov. Matem., 2023, no. 11, 86–91
N. F. Abuzyarova, “Invariant Subspaces in Nonquasianalytic Spaces of Ω-Ultradifferentiable Functions on an Interval”, Russ Math., 67:11 (2023), 75
A. S. Krivosheev, O. A. Krivosheeva, “The distribution of singular points of the sum of a series of exponential monomials on the boundary of its domain of convergence”, Sb. Math., 211:1 (2020), 55–114
S. N. Melikhov, “Coefficients of exponential series for analytic functions and the Pommiez operator”, J. Math. Sci. (N. Y.), 257:2 (2021), 206–245
S. G. Merzlyakov, “Systems of convolution equations in complex domains”, Ufa Math. J., 10:2 (2018), 78–92
O. A. Krivosheeva, A. S. Krivosheev, “Singular points for the sum of a series of exponential monomials”, Probl. anal. Issues Anal., 7(25), spetsvypusk (2018), 72–87
O. A. Ivanova, S. N. Melikhov, “Kommutant operatora Pomme v prostranstve tselykh funktsii eksponentsialnogo tipa i polinomialnogo rosta na veschestvennoi pryamoi”, Vladikavk. matem. zhurn., 20:3 (2018), 48–56
N. F. Abuzyarova, “Spectral Synthesis for the Differentiation Operator in the Schwartz Space”, Math. Notes, 102:2 (2017), 137–148
O. A. Krivosheeva, “Invariant subspaces with zero density spectrum”, Ufa Math. J., 9:3 (2017), 100–108
Olga A. Ivanova, Sergej N. Melikhov, “On the Completeness of Orbits of a Pommiez Operator in Weighted (LF)-Spaces of Entire Functions”, Complex Anal. Oper. Theory, 11:6 (2017), 1407
O. A. Krivosheeva, A. S. Krivosheev, “Singular points of the sum of a Dirichlet series on the convergence line”, Funct. Anal. Appl., 49:2 (2015), 122–134
T. A. Volkovaya, “Sintez v polinomialnom yadre dvukh analiticheskikh funktsionalov”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 14:3 (2014), 251–262
O. A. Krivosheyeva, “Singular points of the sum of exponential monomials series on the boundary of convergence domain”, St. Petersburg Math. J., 23:2 (2012), 321–350
O. A. Krivosheeva, “Osobye tochki summy ryada eksonent na granitse oblasti skhodimosti”, Ufimsk. matem. zhurn., 1:4 (2009), 78–109
V. V. Napalkov, V. A. Tarov, “On Some Properties of Subharmonic Functions and Entire Functions of Order Zero”, Journal of Mathematical Sciences, 155:1 (2008), 89–104
B. N. Khabibullin, “Spectral synthesis for the intersection of invariant subspaces of holomorphic functions”, Sb. Math., 196:3 (2005), 423–445
B. N. Khabibullin, “Dva obschikh usloviya nedopustimosti spektralnogo sinteza dlya invariantnykh podprostranstv golomorfnykh funktsii”, Vladikavk. matem. zhurn., 7:3 (2005), 71–78
I. F. Krasichkov-Ternovskii, “Spectral synthesis and analytic continuation”, Russian Math. Surveys, 58:1 (2003), 31–108
Citation in format AMSBIB
Contact us: