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On weighted polynomial
approximation of entire functions
Bert Alan Taylor |
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Vol. 36 (1971), No. 2, 523–539
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Abstract |
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An existence theorem for the ∂ operator is used here to prove some results on weighted approximation of entire functions. Theorem 2 shows that if ϕ is a convex function on Cn = R2n such that the Hilbert space of all entire functions f with ∫ |f|2e−∅dλ < +∞ ( dλ Lebesgue measure) contains the polynomials, then the polynomials are dense in this Hilbert space. Two approximation theorems are also given which are related to the theory of quasi-analytic functions. |
Mathematical Subject Classification
Primary: 46.30
Secondary: 32.00
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Milestones
Received: 23 April 1969
Published: 1 February 1971
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Authors |
| Bert Alan Taylor | |
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