### Linear Functionals in Some Spaces of Entire Functions of Finite Order

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#### Abstract

We consider the the linear topology space of entire functions of a proximate order and normal type with respect to the proximate order. We obtain the form of continuous linear functional on this space.

#### Keywords

Entire function, proximate order, continuous linear functional.

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PDF#### References

Levin, B.Ya., Distribution of Zeros of Entire Functions, English revised edition Amer. Math.Soc, Providence, RI, 523pp. MR 81k:30011, 1980.

Bingham N.H., Goldie C.M., Teugels J.L., Regular variation, Cambridge university press, Cambridge, London, New-York, New Rochele, Melburn, Sydney, 1987.

Leont'ev, A.F., Obobshcheniye ryadov e'ksponent, Nauka, (Russian), 1981.