Uniform harmonic approximation of bounded functions

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

UNIFORM APPROXIMATION BY b – HARMONIC FUNCTIONS

The Mergelyan and Ahlfors-Beurling estimates for the Cauchy transform give quantitative information on uniform approximation by rational functions with poles off K. We will present an analogous result for an integral transform on the unit sphere in C2 introduced by Henkin, and show how it can be used to study approximation by functions that are locally harmonic with respect to the Kohn Laplacia...

متن کامل

Uniform Rectifiability, Carleson Measure Estimates, and Approximation of Harmonic Functions

Let E ⊂ Rn+1, n ≥ 2, be a uniformly rectifiable set of dimension n. Then bounded harmonic functions in Ω := Rn+1 \ E satisfy Carleson measure estimates, and are “ε-approximable”. Our results may be viewed as generalized versions of the classical F. and M. Riesz theorem, since the estimates that we prove are equivalent, in more topologically friendly settings, to quantitative mutual absolute con...

متن کامل

The best uniform polynomial approximation of two classes of rational functions

In this paper we obtain the explicit form of the best uniform polynomial approximations out of Pn of two classes of rational functions using properties of Chebyshev polynomials. In this way we present some new theorems and lemmas. Some examples will be given to support the results.

متن کامل

Approximation by Bounded Analytic Functions: Uniform Convergence as Implied by Mean Convergence^) By

In three recent notes [1], [2], [3] I have discussed uniform convergence by polynomials (in the complex variable) to a given function as a consequence of convergence in the mean of those polynomials to the given function, and also convergence in the mean of one order as a consequence of convergence in the mean of a lower order. The present note contains analogs of those results, but now for app...

متن کامل

L-bounded Point Evaluations for Polynomials and Uniform Rational Approximation

A connection is established between uniform rational approximation and approximation in the mean by polynomials on compact nowhere dense subsets of the complex plane C. Peak points for R(X) and bounded point evaluations for Hp(X, dA), 1 ≤ p < ∞, play a fundamental role.

متن کامل

ذخیره 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: Transactions of the American Mathematical Society

سال: 1996

ISSN: 0002-9947,1088-6850

DOI: 10.1090/s0002-9947-96-01455-9