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Natural exponential families of probability distributions and exponential-polynomial approximation

✍ Scribed by Clyde Martin; Victor Shubov


Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
877 KB
Volume
59
Category
Article
ISSN
0096-3003

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Forward and Converse Theorems of Polynom
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We consider exponential weights of the form w :=e &Q on (&1, 1) where Q(x) is even and grows faster than (1&x 2 ) &$ near \1, some $>0. For example, we can take where exp k denotes the kth iterated exponential and exp 0 (x)=x. We prove Jackson theorems in weighted L p spaces with norm & fw& Lp(&1,

Forward and Converse Theorems of Polynom
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We consider exponential weights of the form w :=e &Q on [&1, 1] where Q(x) is even and grows faster than (1&x 2 ) &$ near \1, some $>0. For example, we can take where exp k denotes the kth iterated exponential and exp 0 (x)=x. We prove converse theorems of polynomial approximation in weighted L p s