Definable smoothing of continuous functions
نویسندگان
چکیده
منابع مشابه
Definable Smoothing of Continuous Functions
Let R be an o-minimal expansion of a real closed field. Given definable continuous functions f : U → R and : U → (0,+∞), where U is an open subset of Rn, we construct a definable Cm-function g : U → R with |g(x)− f(x)| < (x) for all x ∈ U . Moreover, we show that if f is uniformly continuous, then g can also chosen to be uniformly continuous.
متن کاملDefinable Smoothing of Lipschitz Continuous Functions
Let M be an o-minimal structure over the real closed field R. We prove the definable smoothing of definable Lipschitz continuous functions. In the case of Lipschitz functions of one variable we are even able to preserve the Lipschitz constant.
متن کاملSheaves of Continuous Definable Functions
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive...
متن کاملPhase smoothing functions for continuous phase modulation
| In this paper, the problem of signal design for continuous phase modulation is examined. Using the performance measures of e ective bandwidth and minimum distance, \optimal" signal shapes are calculated for various receiver observation intervals for full and partial response signalling. For the partial response case, the optimization could only be done for a receiver observation interval of o...
متن کاملDefinable functions continuous on curves in o-minimal structures
We give necessary and sufficient conditions on a non-oscillatory curve in an o-minimal structure such that, for any bounded definable function, there exists a definable closed set containing an initial segment of the curve on which the function is continuous. This question is translated into one on types: What are the conditions on an n-type such that, for any bounded definable function, there ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2013
ISSN: 0019-2082
DOI: 10.1215/ijm/1415023511