Cyclic Vectors and Invariant Subspaces of the Backward Shift Operator in Schwartz Modules

1. O. A. Ivanova and S. 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), 1407–1424.

   Article  MATH  Google Scholar 

2. O. A. Ivanova and S. N. Melikhov, “On invariant subspaces of the Pommiez operator in spaces of entire functions of exponential type”, Itogi Nauki i Tekhn. Ser. Sovr. Mat. i Ee Pril. Temat. Obz., no. 142, VINITI Ross. Akad. Nauk, Moscow, 2017, с. 111–120; English transl.: J. Math. Sci., 241:6 (2019), 760–769.

   Article  MATH  Google Scholar 

3. J. Mikusiński, “Convolution approximation and shift approximation”, Studia Math., 28 (1966), 1–8.

   Article  MATH  Google Scholar 

4. M. T. Karaev, “Closed ideals in \(C^\infty\) with Duhamel product as multiplication”, J. Math. Anal. Appl., 300:2 (2004), 297–302.

   Article  MATH  Google Scholar 

5. V. V. Zharinov, “Compact families of locally convex topological vector spaces, Fréchet–Schwartz and dual Fréchet–Schwartz spaces”, Usp. Mat. Nauk, 34:4(208) (1979), 97–131; English transl.: Russian Math. Surveys, 34:4 (1979), 105–143.

   MATH  Google Scholar 

6. R. Meise and D. Vogt, Introduction to Functional Analysis, Clarendon Press, Oxford Univ. Press, New York, 1997.

   MATH  Google Scholar 

7. L. Hörmander, The Analysis of linear Partial Differential Operators I, Springer-Verlag, Berlin, 1983.

   MATH  Google Scholar 

8. R. Meise and B. A. Tayhor, “Whitney’s extension theorem for ultradifferentiable functions of Beurling type”, Ark. Mat., 26:2 (1988), 265–287.

   Article  MATH  Google Scholar 

9. A. P. Robertson and W. J. Robertson, Topological Vector Spaces, Cambridge Univ. Press, Cambridge, 1964.

   MATH  Google Scholar 

10. O. A. Ivanova and S. N. Melikhov, “On A. F. Leont’ev’s interpolating function”, Ufimsk. Mat. Zh., 6:3 (2014), 17–27; English transl.: Ufa Math. J., 6:3 (2014), 17–27.

    Article  Google Scholar 

11. H. Whitney, “Analytic extensions of differentiable functions defined in closed sets”, Trans. Amer. Math. Soc., 36 (1934), 63–89.

    Article  MATH  Google Scholar 

12. B. Ya. Levin, Distribution of Roots of Entire Functions, Fizmatlit, Moscow, 1956 (Russian).

    Google Scholar 

13. P. Schapira, Theories des Hyperfonctions, Springer-Verlag, Berlin, 1970.

    Book  MATH  Google Scholar 

14. L. Hörmander, “Remarks on Holmgren‘s uniqueness theorem”, Ann. Inst. Fourier, 43:5 (1993), 1223–1251.

    Article  MATH  Google Scholar 

15. O. A. Ivanova and S. N. Melikhov, “The commutant of the Pommiez operator in a space of entire functions of exponential type and polynomial growth on the real line”, Vladikavkaz. Mat. Zh., 20:3 (2018), 48–56.

    MATH  Google Scholar 

16. O. A. Ivanova and S. N. Melikhov, “On operators which commute with the Pommiez type operator in weighted spaces of entire functions”, Algebra i Analiz, 28:2 (2016), 114–137; English transl.: St. Petersburg Math. J., 28:2 (2017), 209–224.

    Google Scholar 

17. A. Aleman and B. Korenblum, “Derivation-invariant subspaces of \(C^\infty\)”, Comput. Methods Funct. Theory, 8:2 (2008), 493–512.

    Article  MATH  Google Scholar 

18. N. F. Abuzyarova, “Spectral synthesis in the Schwartz space of infinitely differentiable functions”, Dokl. Akad. Nauk, 457:5 (2014), 510–513; English transl.: Dokl. Math., 90:1 (2014), 479–482.

    MATH  Google Scholar 

19. A. Aleman, A. Baranov, and Yu. Belov, “Subspaces of \(C^\infty\) invariant under the differentiation”, J. Funct. Analysis, 268:8 (2015), 2421–2439.

    Article  MATH  Google Scholar 

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