Scattering on p-adic graphs

✍ Scribed by R.V. Romanov; G.E. Rudin

• Book ID: 104353064
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 666 KB
• Volume: 34
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(97)00155-7

✦ Synopsis

The scattering problem on the Bruhat-Tits tree and its quotient spaces realizing the p-adic Riemann surfaces is studied. The spectral decomposition of the corresponding Laplace-Beltrami operator is constructed. The stationary S-matrix is obtained and the Lax-Phillips scattering theory for the problem is developed in a closed form. The Eisenstein series technique is applied to 1-1oop case. The analytical structure of the scattering matrix for joint spherical functions is described.