On the Distribution of Zeros and Poles of Rational Approximants on Intervals
Keyword(s):
The distribution of zeros and poles of best rational approximants is well understood for the functions , . If is not holomorphic on , the distribution of the zeros of best rational approximants is governed by the equilibrium measure of under the additional assumption that the rational approximants are restricted to a bounded degree of the denominator. This phenomenon was discovered first for polynomial approximation. In this paper, we investigate the asymptotic distribution of zeros, respectively, -values, and poles of best real rational approximants of degree at most to a function that is real-valued, but not holomorphic on . Generalizations to the lower half of the Walsh table are indicated.
1999 ◽
Vol 98
(1)
◽
pp. 104-116
◽
2015 ◽
Vol 16
(2)
◽
pp. 167-185
◽
2013 ◽
Vol 24
(07)
◽
pp. 1350051
◽
2003 ◽
Vol 150
(1)
◽
pp. 57-70
◽
1994 ◽
Vol 341
(2)
◽
pp. 881-894
◽
2001 ◽
Vol 110
(1)
◽
pp. 88-108
◽
2001 ◽
Vol 108
(1)
◽
pp. 53-96
◽