Definable smoothing of Lipschitz continuous functions
نویسندگان
چکیده
منابع مشابه
Definable 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 کاملDefinable 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 کاملExtension of P-adic Definable Lipschitz Functions
Write OK for the valuation ting, MK for the maximal ideal of K and kK for the residue field. Let us fix $ some uniformizer of K. We denote by acm : K → OK/(MK) the map sending some nonzero x ∈ K to x$−ord(x) mod MK , and sending zero to zero. This is a definable map. We denote by RV the union of K×/(1 +MK) and {0} and by rv : K → RV the quotient map. More generally, if m ∈ N∗, we set RVm = K×/(...
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 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: 2008
ISSN: 0019-2082
DOI: 10.1215/ijm/1248355351