Local description of entire functions. Submodules of rank 1

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2016.2.7385 Local description of entire functions. Submodules of rank 1 Volkovaya T. A. , Shishkin, A. B. Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 2. Abstract: Submodule in the module of entire functions is called ample, if this submodule coincides with its local hull. Ampleness splits in three separate properties: intensity, stability and saturation. In the article submodules of entire functions are investigated for the presence of these properties. Particular attention is paid to submodules of rank 1 Keywords: submodules of entire functions, local submodules, local shell, local description, ampleness, intensity, stability, saturation, criterion of ampleness Language: Russian Download the full text For citation: Volkovaya T. A., Shishkin A. B. Local description of entire functions. Submodules of rank 1. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 2, pp.14-28. DOI 10.23671/VNC.2016.2.7385 + References 1. Krasichkov-Ternovskij I. F. Local description of closed ideals and submodules of analytic functions of one variable. I. Mathematics of the USSR-Izvestiya, 1980, vol. 14, no. 1, pp. 41-60. 2. Krasichkov-Ternovskij I. F. Local description of closed ideals and submodules of analytic functions of one variable. II. Mathematics of the USSR-Izvestiya, 1980, vol. 14, no. 2, pp. 289-316. 3. Krasichkov-Ternovskij I. F. Abstract methods for a local description of closed submodules of analytic functions. Mathematics of the USSR-Sbornik, 1992, vol. 71, no. 2, pp. 481-497. 4. Shishkin A. B. Local description of closed submodules in a special module of entire functions of exponential type. Mathematical Notes, 1989, vol. 46, no. 6, pp. 952-956. 5. Shishkin A. B. Spectral synthesis for an operator generated by multiplication by a power of the independent variable. Mathematics of the USSR-Sbornik, 1992, vol. 73, no. 1, pp. 211-229. 6. Krasichkov-Ternovskij I. F. Spectral synthesis in a complex domain for a differential operator with constant coefficients. I: a duality theorem. Mathematics of the USSR-Sbornik, 1993, vol. 74, no. 2, pp. 309-335. 7. Shishkin A. B. Spectral synthesis for systems of differential operators with constant coefficients. Duality theorem. Sb. Math., 1998, vol. 189, no. 9, pp. 1423-1440. 8. Chernyshev A. N. Spektral'nyj Sintez dlja Differencial'nogo Operatora Beskonechnogo Porjadka s Postojannymi Kojefficientami: Dis. ... Kand. Fiz.-Mat. Nauk, Armavir, 2004, 100 p. (Russian). 9. Pis'mennyj R. G. Glavnye Podmoduli i Invariantnye Podprostranstva Analiticheskih Funkcij: Dis. ... Kand. Fiz.-Mat. Nauk, Slavjansk-na-Kubani, 2010, 104 p. (Russian). 10. Volkovaya T. A., Shishkin A. B. Local description of entire functions. Mat. Forum. Vol. 8, part 1. Issledovanija po Mat. Analizu [Math. Forum. Vol. 8, part 1. Studies on Math. Analysis], Vladikavkaz, UMI VNC RAN i RSO-A, 2014, pp. 212-223 (Russian). 11. Shishkin A. B. Projective and injective descriptions in the complex domain. Duality. Izv. Saratov Univ. (N.S.). Ser. Math. Mech. Inform., 2014, vol. 14, no. 1, pp. 47-65 (Russian). The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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