Asgeirsson's Mean Value Theorem and Related Identities

✍ Scribed by Lars Hörmander

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 212 KB
• Volume: 184
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2001.3743

✦ Synopsis

Asgeirsson's mean value theorem states that if u satisfies the ultrahyperbolic differential equation (2

We extend this to solutions of the inhomogeneous equation by proving that f =(2 x &2 y ) + R where

• on R are defined by / a + (t)=t a + Â1(a+1) when Re a>&1 and then continued analytically to all a # C. This formula is closely related to the fundamental solution of the wave equation in R &+1 . Similar identities are given for arbitrary indefinite nonsingular real quadratic forms in R 2& . This work was originally motivated by the progressive solutions of the wave equation given by G. Friedlander and M. Riesz.

2001