NEW THEOREMS ON THE MEAN FOR SOLUTIONS OF THE HELMHOLTZ-EQUATION

被引：4
作者：
VOLCHKOV, VV
机构：
来源：
RUSSIAN ACADEMY OF SCIENCES SBORNIK MATHEMATICS | 1994年 / 79卷 / 02期
关键词：
D O I：
10.1070/SM1994v079n02ABEH003500
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is proved that the solutions of the equation Delta u+u = 0 are characterized by vanishing of integrals over all balls in R(n) with radii belonging to the zero set of the Bessel function J(n/2). This result enables us to get a solution of the Pompeiu problem on the class of functions of slow growth in terms of approximation in L(R(n)) by linear combinations with special radii.
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页码：281 / 286
页数：6
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