منابع مشابه
Invariant Mean Value Property and Harmonic Functions
We give conditions on the functions σ and u on R such that if u is given by the convolution of σ and u, then u is harmonic on R.
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چکیده ندارد.
Harmonic functions via restricted mean-value theorems
Let f be a function on a bounded domain Ω ⊆ R and δ be a positive function on Ω such that B(x, δ(x)) ⊆ Ω. Let σ(f)(x) be the average of f over the ball B(x, δ(x)). The restricted mean-value theorems discuss the conditions on f, δ, and Ω under which σ(f) = f implies that f is harmonic. In this paper, we study the stability of harmonic functions with respect to the map σ. One expects that, in gen...
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For n ≥ 2, let Bn denote the unit ball in R, and for p ≥ 1 let L denote the Banach space of p-summable functions on Bn. Let L p h(Bn) denote the subspace of harmonic functions on Bn that are p-summable. When n = 2, we often write D instead of B2, and we let A denote the Bergman space of analytic functions in L. Let ω be a function in L. We are interested in finding the best approximation to ω i...
متن کاملOn The Mean Convergence of Biharmonic Functions
Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...
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ژورنال
عنوان ژورنال: Aequationes mathematicae
سال: 2017
ISSN: 0001-9054,1420-8903
DOI: 10.1007/s00010-017-0498-3