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	Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. 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). ← Contents of issue


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