Approximation by Entire Functions on Unbounded Domains in Cn
نویسندگان
چکیده
منابع مشابه
On the approximation of entire functions over Carathéodory domains
Let D be a Carathéodory domain. For 1 ≤ p ≤ ∞, let Lp(D) be the class of all functions f holomorphic in D such that ‖f‖D,p = [ 1 A R R D |f(z)| p dx dy]1/p < ∞, where A is the area of D. For f ∈ Lp(D), set E n(f) = inf t∈πn ‖f − t‖D,p ; πn consists of all polynomials of degree at most n. In this paper we study the growth of an entire function in terms of approximation error in Lp-norm on D.
متن کاملInterpolation and Approximation by Entire Functions
In this note we study the connection between best approximation and interpolation by entire functions on the real line. A general representation for entire interpolants is outlined. As an illustration, best upper and lower approximations from the class of functions of fixed exponential type to the Gaussian are constructed. §1. Approximation Background The Fourier transform of φ ∈ L(R) is define...
متن کاملOne-sided approximation by entire functions
Let f : R→ R have an nth derivative of finite variation Vf(n) and a locally absolutely continuous (n− 1)st derivative. Denote by E±(f, δ)p the error of onesided approximation of f (from above and below, respectively) by entire functions of exponential type δ > 0 in Lp(R)–norm. For 1 ≤ p ≤ ∞ we show the estimate E±(f, δ)p ≤ C n π1/pVf(n)δ −n− 1 p , with constants Cn > 0.
متن کاملSolving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation
In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...
متن کاملApproximation of Some Diffusion Evolution Equations in Unbounded Domains by Hermite Functions
Spectral and pseudospectral approximations of the heat equation are analyzed. The solution is represented in a suitable basis constructed with Hermite polynomials. Stability and convergence estimates are given and numerical tests are discussed. Introduction Many physical models involve the determination of the solution of a partial differential equation in an unbounded domain. The conditions at...
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 Approximation Theory
سال: 1993
ISSN: 0021-9045
DOI: 10.1006/jath.1993.1070