Let [ f m ; m # N] be a sequence of functions from [0, ) to a Banach space E. We give a new and essential condition on f m , which is weaker than the usual ``local Lipschitz continuity'' condition, ensuring that the convergence of f m is equivalent to the convergence of their Laplace transforms. Thi
On the Convergence and Approximation of Integrated Semigroups
โ Scribed by C. Lizama
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 427 KB
- Volume
- 181
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
For a general approximation process we formulate theorems concerning rates of convergence, including theorems about saturation class, non-optimal rates, and sharpness of non-optimal convergence. The general results are then applied to n-times integrated semigroups and cosine functions, yielding some
This paper investigates the convergence condition for the polynomial approximation of rational functions and rational curves. The main result, based on a hybrid expression of rational functions (or curves), is that two-point Hermite interpolation converges if all eigenvalue moduli of a certain r\_r
Let (P t ) t 0 and (P t ) t 0 be two diffusion semigroups on R d (d 2) associated with uniformly elliptic operators L={ } (A{) and L ={ } (A {) with measurable coefficients A=(a ij ) and A =(a~i j ), respectively. The corresponding diffusion kernels are denoted by p t (x, y) and p~t(x, y). We derive