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The range of an operator of convolution type. (English) Zbl 0404.47023
##### MSC:
 47Gxx Integral, integro-differential, and pseudodifferential operators 42A85 Convolution, factorization for one variable harmonic analysis
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##### References:
 [1] O. V. Epifanov, ”On the problem of the surjectivity of a convolution operator in convex domains,” Mat. Zametki,16, No. 3, 415–422 (1974). [2] V. A. Tkachenko, ”On operators of convolution type in spaces of analytic functionals,” Dokl. Akad. Nauk SSSR,219, No. 3, 555–557 (1974). · Zbl 0325.47034 [3] L. Gruman, ”Infinite order differential equations in Banach spaces of entire functions,” J. London Math. Soc.,7, No. 3, 492–500 (1974). · Zbl 0269.35072 · doi:10.1112/jlms/s2-7.3.492 [4] D. A. Raikov, ”Inductive and protective limits with completely continuous maps,” Dokl. Akad. Nauk SSSR,113, No. 5, 984–986 (1957). · Zbl 0079.32204 [5] H. Schaeffer, Topological Vector Spaces, Springer-Verlag, New York. · Zbl 0434.51007 [6] G. Köthe, ”Dualität in der Funktionentheorie,” J. Reine Angew. Math.,191, 30–49 (1953). · Zbl 0050.33502 · doi:10.1515/crll.1953.191.30 [7] O. V. Epifanov and A. A. Lenev, ”On the solvability of an integral equation in spaces of analytic functions,” in: Math. Analysis and Its Applications [in Russian], Vol. VI Rostov State Univ., pp. 258–261. · Zbl 0346.45002 [8] B. J. Levin, Distribution of Zeros of Entire Functions, Amer. Math. Soc. (1972). [9] I. F. Krasichkov-Ternovskii, ”Invariant subspaces of analytic functions. II. Spectral synthesis of convex domains,” Mat. Sb.,88, No. 1, 3–30 (1973). [10] V. A. Tkachenko, ”On spectral decompositions in spaces of analytic functionals,” Dokl. Akad. Nauk SSSR,217, No. 5, 1017–1020 (1974). [11] V. A. Tkachenko, ”On spectral synthesis in spaces of analytic functionals,” Dokl. Akad. Nauk SSSR,223, No. 2, 307–309 (1975). · Zbl 0327.46034 [12] O. V. Epifanov, ”Solvability of a convolution equation in convex domains,” Mat. Zametki,15, No. 5, 787–796 (1975). · Zbl 0314.46050 [13] A. Martineau, ”Equations différentielles d’ordre infini,” Bull. Soc. Math. France,95, 109–154 (1967). · Zbl 0167.44202 [14] A. A. Gol’dberg and I. V. Ostrovskii, Distributions of Values of Meromorphic Functions [in Russian], Nauka, Moscow (1970). [15] Yu. N. Frolov, ”On inhomogeneous equations of infinite order involving distribution derivatives,” Vestn. Mosk. Gos. Univ., Ser. Mat. Mekh., No. 4, 3–12 (1960). [16] A. F. Leont’ev, ”Series of Dirichlet polynomials and their generalizations,” Tr. Mat. Inst., Akad. Nauk SSSR,39 (1951). [17] A. F. Leont’ev, ”On the convergence of a sequence of Dirichlet polynomials,” Dokl. Akad. Nauk SSSR,108, No. 1, 23–26 (1956). · Zbl 0073.29302 [18] V. S. Azarin, ”On a characteristic property of functions of completely regular growth inside an angular sector,” Teor. Funkts., Funkts. Anal. Prilozhen.,2, 55–66 (1966). [19] V. S. Azarin, ”On rays of completely regular growth of an entire function,” Mat. Sb.,79, No. 4, 463–476 (1969). [20] V. I. Protasov, ”On solutions of linear equations of infinite order involving distribution derivatives,” Dokl. Akad. Nauk SSSR,154, No. 6, 1273–1275 (1964). [21] V. I. Protasov, ”The Cauchy problem for a linear differential equation of infinite order,” Dokl. Akad. Nauk SSSR,164, No. 4, 743–745 (1965). · Zbl 0151.11004
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