Restricted log-exp-analytic functions and some differentiability results
نویسندگان
چکیده
In this article, we define restricted log-exp-analytic functions as compositions of log-analytic and exponentials locally bounded functions. We prove that the derivative a function is again such exhibits strong quasianalytic properties. establish parametric version Tamm’s theorem for class
منابع مشابه
Growth Estimates for Exp-Log Functions
Exp-log functions are those obtained from the constant 1 and the variable X by means of arithmetic operations and the function symbols exp() and logll. This paper gives an explicit algorithm for determining eventual dominance of these functions modulo an oracle for deciding zero equivalence of constant terms. This also provides another proof that the dominance problem for exp-log functions is T...
متن کاملTwofold exp and log
This article is about twofold arithmetic [1, 2]. Here I introduce algorithms and experimental code for twofold variant of C/C++ standard functions exp() and log(), and expm1() and log1p(). Twofold function y0 + y1 ≈ f(x0 + x1) is nearly 2x-precise so can assess accuracy of standard one. Performance allows assessing on-fly: twofold texp() over double is ~10x times faster than expq() by GNU quadm...
متن کاملSome Results on Bernstein-sato Polynomials for Parametric Analytic Functions
This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in the case of one function. We also make an extensive study of an example for which we give an expression of a generic (and under some conditions, a relative) B...
متن کاملRestricted Ideals in Rings of Analytic Functions
Introduction. Let Y be a connected, noncompact Riemann surface, and let A be the ring of all analytic functions on Y. It is known that the ideal theory of the ring A is strikingly similar to the ideal theory of the ring C(X) of all real valued continuous functions on a completely regular topological space X. We show that locally much of the ideal theory of A can be recovered from the ideal theo...
متن کاملAsymptotic Expansions of exp - log
We give an algorithm to compute asymptotic expansions of exp-log functions. This algorithm automatically computes the necessary asymptotic scale and does not suuer from problems of indeenite cancellation. In particular, an asymptotic equivalent can always be computed for a given exp-log function. D eveloppements asymptotiques de fonctions exp-log R esum e Nous pr esentons un algorithme pour le ...
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: 2022
ISSN: ['1945-6581', '0019-2082']
DOI: https://doi.org/10.1215/00192082-10234104