Uniform approximations by holomorphic functions
نویسندگان
چکیده
منابع مشابه
Uniform Approximations for Transcendental Functions
A heuristic method to construct uniform approximations to analytic transcendental functions is developed as a generalization of the Hermite-Padé interpolation to infinite intervals. The resulting uniform approximants are built from elementary functions using known series and asymptotic expansions of the given transcendental function. In one case (Lambert’s W function) we obtained a uniform appr...
متن کاملOn the Uniform Learnability of Approximations to Non-Recursive Functions
Blum and Blum (1975) showed that a class B of suitable recursive approximations to the halting problem is reliably EX-learnable. These investigations are carried on by showing that B is neither in NUM nor robustly EX-learnable. Since the definition of the class B is quite natural and does not contain any self-referential coding, B serves as an example that the notion of robustness for learning ...
متن کاملFrom Holomorphic Functions to Holomorphic Sections
It is a pleasure to have the opportunity in the graduate colloquium to introduce my research field. I am a differential geometer. To be more precise, I am a complex differential geometer, although I am equally interested in real differential geometry. To many people, geometry is a kind of mathematics that is related to length, area, volume, etc. For the Euclidean geometry, this is indeed the ca...
متن کاملApproximating Continuous Functions by Holomorphic and Harmonic Functions
If Q is a Widom domain in the plane (e.g., finitely connected) and / is any bounded harmonic function on Q which is not holomorphic, then we prove the algebra H°°(Sl)[f] contains all the uniformly continuous functions on ÎÎ . The basic tools are the solution of the 5 equation with L°° estimates and some estimates on the level sets of functions in BMOA.
متن کاملBest Approximations by Smooth Functions
THEOREM 1.1 (U. Sattes). Let r > 2 and g E C[O, l]\B$,‘. Then f”EB$’ is a best approximation to g, in L” (such a best approximation necessari/J) exisrs) if and only if there exists a subinterual (a, /?) c IO. 1 I and a positilse integer M > r + 1 for which the following conditions hold (i) f”l,n.ll, is a Perfect spline of degree r with exactly) M ~ r -1 knots arzd I.f”““(s)l = I a. e. on [u,pI....
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: Journal of Functional Analysis
سال: 1975
ISSN: 0022-1236
DOI: 10.1016/0022-1236(75)90047-6