منابع مشابه
On the mean value property of superharmonic and subharmonic functions
Recall that a function u is harmonic (superharmonic, subharmonic) in an open set U ⊂ Rn (n ≥ 1) if u ∈ C2(U) and Δu = 0 (Δu ≤ 0,Δu ≥ 0) on U . Denote by H(U) the space of harmonic functions in U and SH(U) (sH(U)) the subset of C2(U) consisting of superharmonic (subharmonic) functions in U . If A ⊂ Rn is Lebesgue measurable, L1(A) denotes the space of Lebesgue integrable functions on A and |A| d...
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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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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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for xER, 0<t<ex (R denotes an «-dimensionaI region; x and yt are abbreviations for (xi, • • • , x„), (yn, • • • , ytn))We assume that the y<'s span £„ so that I^m^JV. We furthermore assume, without loss of generality, that yi, • • • , y« are linearly independent. Friedman and Littman [5] have recently shown that V consists of polynomials of degrees ^N(N—l)/2. This bound is actually attained whe...
متن کاملMean-value property on manifolds with minimal horospheres
Let (M, g) be a non-compact and complete Riemannian manifold with minimal horospheres and infinite injectivity radius. We prove that bounded functions on (M, g) satisfying the mean-value property are constant. We extend thus a result of the authors in [6] where they proved a similar result for bounded harmonic functions on harmonic manifolds with minimal horospheres. MSC 2000: 53C21 , 53C25.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1987
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1987-0891149-1