Representation of continuous linear operators acting in spaces of analytic functions of several variables.

*(English)*Zbl 0582.47034Translation from Mat. Zametki 35, No.5, 721-727 (Russian) (1984; Zbl 0567.47023).

##### MSC:

47B38 | Linear operators on function spaces (general) |

47F05 | General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX) |

##### Keywords:

topology of compact convergence; representability of an arbitrary continuous linear operator T, acting from a space of functions that are analytic in a polydisc into a space of the same kind, in the form of differential operator of infinite order
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##### References:

[1] | Yu. F. Korobeinik, ?On the question of the representation of an arbitrary linear operator in the form of a differential operator of infinite order,? Mat. Zametki,16, No. 2, 277-283 (1974). |

[2] | S. S. Linchuk, ?On the representation of continuous linear operators acting in spaces of analytic functions,? Manuscript deposited at VINITI, No. 1798-82. |

[3] | G. G. Braichev and V. V. Morzhakov, ?On the applicability of partial differential operators of infinite order,? Mat. Zametki,24, No. 6, 771-777 (1978). |

[4] | Yu. F. Korobeinik, ?The general form of a linear functional in certain spaces of analytic functions and its applications to the theory of differential operators of infinite order,? in: Mathematical Analysis and Its Applications [in Russian], Rostov-on-the-Don (1969), pp. 116-132. |

[5] | V. P. Podporin, ?On the representation of linear operators in the form of differential operators of infinite order,? Sib. Mat. Zh.,17, No. 1, 148-159 (1976). · Zbl 0325.47031 |

[6] | V. P. Podporin, ?On the question of the representation of linear operators in the form of differential operators of infinite order,? Sib. Mat. Zh.,18, No. 6, 1422-1425 (1977). · Zbl 0389.47016 |

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