Filippov Implicit Function Theorem for Quasi-Carathéodory Functions
✍ Scribed by M Dindoš; V Toma
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 162 KB
- Volume
- 214
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
✦ Synopsis
Several Filippov type implicit function theorems are known for Caratheodory Ž .
Ž . Ž . functions f t, x , i.e., all f и, x are measurable and f t, и are continuous. We Ž . prove some generalisations of this theorem supposing only each function f t, и to be quasicontinuous with closed values.
📜 SIMILAR VOLUMES
## Abstract We consider an interpolation problem of Nevanlinna–Pick type for matrix‐valued Carathéodory functions, where the values of the functions and its derivatives up to certain orders are given at finitely many points of the open unit disk. For the non‐degenerate case, i.e., in the particular
## Abstract It is shown that the following conditions are equivalent for the generalized Schur class functions at a boundary point __t__~0~ ∈ 𝕋: 1) Carathéodory–Julia type condition of order __n__; 2) agreeing of asymptotics of the original function from inside and of its continuation by reflection
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