Deduction of L. Hörmander's extension of Ásgeirsson's mean value theorem
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- 作者：Ortner ; Norbert ; Wagner ; Peter
- 关键词：35L82 ; 35B05 ; 35E99 ; 35C05 ; Á ; sgeirsson's mean value theorem ; Ultrahyperbolic equation ; Distribution-valued meromorphic functions
- 刊名：Bulletin des Sciences Mathematiques
- 出版年：2003
- 出版时间：December, 2003
- 年：2003
- 卷：127
- 期：10
- 页码：835-843
- 全文大小：98.8 K
文摘
L. Hörmander's extension of Ásgeirsson's mean value theorem states that if u is a solution of the inhomogeneous ultrahyperbolic equation (Δx−Δy)u=f, x,y
Rν, fE′(R2ν), then Formula Not Shown where t is positive and μt is given explicitly. Whereas L. Hörmander proves this by defining μt without much motivation and then verifying the equation Formula Not Shown the aim of this article is a constructive deduction of a slightly different representation of the distribution μt, viz. μt is the analytic continuation of Formula Not Shown into the value z=ν, where A=t4−2t2(
x2+y2)+(x2−y2)2.
Rν, fE′(R2ν), then Formula Not Shown where t is positive and μt is given explicitly. Whereas L. Hörmander proves this by defining μt without much motivation and then verifying the equation Formula Not Shown the aim of this article is a constructive deduction of a slightly different representation of the distribution μt, viz. μt is the analytic continuation of Formula Not Shown into the value z=ν, where A=t4−2t2(x2+y2)+(x2−y2)2.