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Transformation operator in spaces of entire functions. (English) Zbl 0431.30040

MSC:

30H05 Spaces of bounded analytic functions of one complex variable
47E05 General theory of ordinary differential operators
46E10 Topological linear spaces of continuous, differentiable or analytic functions

Citations:

Zbl 0405.30037
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References:

[1] J. Delsartes, ?Sur certaines transformations fonctionelles relative aux equations lineaires aux derivees partielles du second ordre,? C. R. Acad. Sci. Paris,206, No. 1, 178-182 (1938).
[2] J. Delsartes and J. L. Lions, ?Transmutations d’opèrateurs differentielles dans le domain complexe,? Comment. Math. Helv.,32, No. 2, 113-128 (1957). · Zbl 0080.29501 · doi:10.1007/BF02564574
[3] L. A. Sakhnovich, ?Inverse problem for differential operators of order n>2 with analytic coefficients,? Mat. Sb.,46, No. 1, 61-76 (1958). · Zbl 0084.28403
[4] M. K. Fage, ?Operator analytic functions of one independent variable,? Dokl. Akad. Nauk SSSR,112, No. 6, 1008-1011 (1957). · Zbl 0085.04601
[5] M. K. Fage, ?Operator analytic functions of one independent variable,? Tr. Mosk. Mat. O-va, No. 7, 227-268 (1958). · Zbl 0084.05304
[6] V. I. Matsaev, ?On the existence of a transformation operator for differential operators of higher order,? Dokl. Akad. Nauk SSSR,130, No. 3, 499-502 (1960). · Zbl 0089.06603
[7] B. M. Levitan, Theory of Generalized Translation Operators [in Russian], Nauka, Moscow (1973). · Zbl 0273.34010
[8] A. O. Gel’fond and A. F. Leont’ev, ?On a generalization of Fourier series,? Mat. Sb.,29, No. 3, 477-500 (1951).
[9] M. M. Dzhrbashyan, Integral Representations and Transformations of Functions in the Complex Domain [in Russian], Nauka, Moscow (1966). · Zbl 0148.30002
[10] V. A. Tkachenko, ?On a transformation operator in spaces of entire functions of finite order,? in: Theory of Functions, Functional Analysis, and Their Applications [in Russian], No. 22 (1975), pp. 154-159.
[11] I. F. Krasichkov, ?On closed ideals in locally convex algebras of entire functions,? Izv. Akad. Nauk SSSR, Ser. Mat.31, No. 1, 37-60 (1967). · Zbl 0152.13203
[12] I. F. Krasichkov, ?On closed ideals in locally convex algebras of entire functions,? Izv. Akad. Nauk SSSR, Ser. Mat.,32, No. 5, 1024-1032 (1968). · Zbl 0169.17803
[13] B. A. Taylor, ?Some locally convex spaces of entire functions,? Proc. Symp. Pure Math., II. Entire Functions and Related Parts Anal., Am. Math. Soc. Publ., 431-468 (1968). · Zbl 0181.13304
[14] I. F. Krasichkov, ?On closed ideals in locally convex algebras of entire functions, algebras of minimal type,? Sib. Mat. Zh.,9, No. 1, 77-96 (1968). · Zbl 0161.10804
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