منابع مشابه
On 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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We consider bivariate mean-value interpolationproblem, where the integrals over circles are interpolation data. In this case the problem is described over circles of the same radius and with centers are on astraight line and it is shown that in this case the interpolation is not correct.
متن کاملOn 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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exists . The question of the existence of the mean value M(g) has been much studied, but it has been solved only for certain subclasses . One of the definite results is the following theorem, due to H . Delange [2] (throughout the paper, p denotes a prime, and E and n denote a sum ana a product, respectively, taken over all primes) : p . p If g(n) is a strongly multiplicative number-theoretical...
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In this paper we consider multivariate Lagrange mean-value interpolation problem, where interpolation parameters are integrals over spheres. We have concentric spheres. Indeed, we consider the problem in three variables when it is not correct.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1948
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1948-09077-2