Let B^pΩ, 1 ≤ p 〈 ∞, be the space of all bounded functions from Lp（R） which can be extended to entire functions of exponential type Ω. The uniform error bounds for truncated Whittaker-Kotelnikov-Shannon series ...Let B^pΩ, 1 ≤ p 〈 ∞, be the space of all bounded functions from Lp（R） which can be extended to entire functions of exponential type Ω. The uniform error bounds for truncated Whittaker-Kotelnikov-Shannon series based on local sampling are derived for functions f ∈ B^pΩ without decay assumption at infinity. Then the optimal bounds of the aliasing error and truncation error of Whittaker-Kotelnikov-Shannon expansion for non-bandlimited functions from Sobolev classes L/（Wp（R）） are determined up to a logarithmic factor.展开更多
Let f∈L<sub>p</sub><sup>r</sup>（R）,1【p【∞,r∈N),the bound for aliasing of function fin L<sub>p</sub>—metricesis given in[1].From embedding Theorem and Stein inequality,it foll...Let f∈L<sub>p</sub><sup>r</sup>（R）,1【p【∞,r∈N),the bound for aliasing of function fin L<sub>p</sub>—metricesis given in[1].From embedding Theorem and Stein inequality,it follows,that if f∈L<sub>p</sub><sup>r</sup>（R）,1【p【∞,then f∈L<sub>q</sub><sup>r</sup>（R）,1【p【q≤∞ and f<sup>（k）</sup>∈L<sub>p</sub>（R）∩L<sub>q</sub>（R）,k=0,1,…,r-1.In this paper,we con-tinued Fang’s work in[1],and obtain the bound for aliasing error of function f∈L<sub>p</sub><sup>r</sup>（R）,1【p【∞,inL<sub>q</sub>-metrices（p≤q≤∞）.And the order is exact when 1【p≤q≤2.展开更多
基金Supported by the National Natural Science Foundation of China (10971251, 11101220 and 11271199)the Program for new century excellent talents in University of China (NCET-10-0513)
文摘Let B^pΩ, 1 ≤ p 〈 ∞, be the space of all bounded functions from Lp（R） which can be extended to entire functions of exponential type Ω. The uniform error bounds for truncated Whittaker-Kotelnikov-Shannon series based on local sampling are derived for functions f ∈ B^pΩ without decay assumption at infinity. Then the optimal bounds of the aliasing error and truncation error of Whittaker-Kotelnikov-Shannon expansion for non-bandlimited functions from Sobolev classes L/（Wp（R）） are determined up to a logarithmic factor.
文摘Let f∈L<sub>p</sub><sup>r</sup>（R）,1【p【∞,r∈N),the bound for aliasing of function fin L<sub>p</sub>—metricesis given in[1].From embedding Theorem and Stein inequality,it follows,that if f∈L<sub>p</sub><sup>r</sup>（R）,1【p【∞,then f∈L<sub>q</sub><sup>r</sup>（R）,1【p【q≤∞ and f<sup>（k）</sup>∈L<sub>p</sub>（R）∩L<sub>q</sub>（R）,k=0,1,…,r-1.In this paper,we con-tinued Fang’s work in[1],and obtain the bound for aliasing error of function f∈L<sub>p</sub><sup>r</sup>（R）,1【p【∞,inL<sub>q</sub>-metrices（p≤q≤∞）.And the order is exact when 1【p≤q≤2.
