Name
Abstract | ||
|---|---|---|
We define the concept of an A-regularized approximation process and prove for it uniform convergence theorems and strong convergence theorems with optimal and non-optimal rates. The sharpness of non-optimal convergence is also established. The general results provide a unified approach to dealing with convergence rates of various approximation processes, and also of local ergodic limits as well. As applications, approximation theorems, and local Abelian and Cesáro ergodic theorems with rates are deduced for n-times integrated solution families for Volterra integral equations, which include n-times integrated semigroups and cosine functions as special cases. Applications to (Y)-semigroups and tensor product semigroups are also discussed. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1006/jath.2001.3650 | Journal of Approximation Theory |
Keywords | Field | DocType |
a-regularized approximation process,local abelian,n-times integrated semigroups,approximation theorem,uniform convergence theorem,various approximation process,strong convergence theorem,convergence rate,tensor product semigroups,non-optimal convergence,ergodic theorem,volterra integral equation,uniform convergence,tensor product | Convergence (routing),Mathematical optimization,Normal convergence,Mathematical analysis,Compact convergence,Ergodic theory,Uniform convergence,Convergence tests,Mathematics,Volterra integral equation,Modes of convergence | Journal |
Volume | Issue | ISSN |
115 | 1 | 0021-9045 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sen-Yen Shaw | 1 | 0 | 0.68 |
| Hsiang Liu | 2 | 0 | 0.34 |