Given an arbitrary set E ⊂ ℝn, n ≥ 2, and a function f: E →ℝ, consider the problem of extending f to a C1 function defined on the entire ℝn. A procedure for determining whether such an extension exists was suggested in 1958 by G. Glaeser. In 2004 C. Fefferman proposed a related procedure for dealing with the much more difficult cases of higher smoothness. The procedures in question require iterated computations of some bundles until the bundles stabilize. How many iterations are needed? We give a sharp estimate for the number of iterations that could be required in the C1 case. Some related questions are discussed.
- Extension of smooth functions
- Glaeser refinements
- Whitney problems