Direct and inverse theorems of rational approximation in the Bergman space
For positive numbers p and {mu} let A{sub p,{mu}} denote the Bergman space of analytic functions in the half-plane {Pi}:={l_brace}z element of C:Imz>0{r_brace}. For f element of A{sub p,{mu}} let R{sub n} (f){sub p,{mu}} be the best approximation by rational functions of degree at most n. Also let {alpha} element of R and {tau}>0 be numbers such that {alpha}+{mu}=1/{tau}-1/p and 1/p+{mu} not element of N. Then the main result of the paper claims that the set of functions f element of A{sub p,{mu}} such that {Sigma}{sub n=1}{sup {infinity}} 1/n (n{sup {alpha}}+{mu}R{sub n} (f){sub p,{mu}}){sup {tau}}<{infinity} is precisely the Besov space B{sub {tau}}{sup {alpha}} of analytic functions in {Pi}. Bibliography: 23 titles.
- OSTI ID:
- 21612601
- Journal Information:
- Sbornik. Mathematics, Vol. 202, Issue 9; Other Information: DOI: 10.1070/SM2011v202n09ABEH004189; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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