Whitney’s Extension Problems and Interpolation of Data
نویسنده
چکیده
Given a function f : E → R with E ⊂ Rn, we explain how to decide whether f extends to a Cm function F on Rn. If E is finite, then one can efficiently compute an F as above, whose Cm norm has the least possible order of magnitude (joint work with B. Klartag).
منابع مشابه
An example related to Whitney extension with almost minimal C norm
We present a counter-example to a certain conjecture that is related to Whitney’s extension problems.
متن کاملEssays in analysis Variations on a theorem of Émile Borel
I. Borel’s Theorem 1. Borel’s Theorem—the elementary proof 2. The proof by functional analysis 3. Why the proof can’t be too elementary 4. A simple application to representation theory 5. The extension theorems of Seeley and Mather 6. References II. Whitney’s differentiable functions 7. Introduction 8. Whitney’s extension theorem 9. Local growth conditions 10. Invariance of Schwartz spaces 11. ...
متن کاملInterpolation of fuzzy data by using flat end fuzzy splines
In this paper, a new set of spline functions called ``Flat End Fuzzy Spline" is defined to interpolate given fuzzy data. Some important theorems on these splines together with their existence and uniqueness properties are discussed. Then numerical examples are presented to illustrate the differences between of using our spline and other interpolations that have been studied before.
متن کاملArcwise Analytic Stratification, Whitney Fibering Conjecture and Zariski Equisingularity
In this paper we show Whitney’s fibering conjecture in the real and complex, local analytic and global algebraic cases. For a given germ of complex or real analytic set, we show the existence of a stratification satisfying a strong (real arc-analytic with respect to all variables and analytic with respect to the parameter space) trivialization property along each stratum. We call such a trivial...
متن کاملEstimating the Real Capacity of Rain Erosion Using GIS (The Fournier Case Study for Isfahan)
Interpolation, the generalization of point data to scatter data, and combining maps are three cases of important applications of GIS. In this study, it has been tried to make the estimation of rain erosion capacity (Fournier Method) more real through using GIS capability in interpolation and the generalization of point data to scatter data. In Fournier method, the rain erosion capacity is calcu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008