The covering number for some Mercer kernel Hilbert spaces

Authors:
Sheng Baohuai;Wang Jianli;Li Ping
Affiliations:
Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, Zhejiang 312000, PR China;Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, Zhejiang 312000, PR China;Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, Zhejiang 312000, PR China
Venue:
Journal of Complexity
Year:
2008

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Abstract

In the present paper, we investigate the estimates for the covering number of a ball in a Mercer kernel Hilbert space on [0,1]. Let P"l(x) be the Legendre orthogonal polynomial of order l, a"l0 be real numbers satisfying @?"l"="0^+^~la"l