Scattering Theory on Locally symmetric Spaces

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Ehyaei, Ahmad Reza | 2010

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 40123 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Razvan, Mohammad Reza
Abstract:
Scattering theory on locally symmetric space first was studied by Peter Lax and Ralph Phillips. They studied the and develop scattering theory on it. Without the Fourier analysis tools this theory was completed with a lot of computations. In this thesis first we try to construct Fourier analysis by definition Fourier transform then by means of new tools we prove very short version of scattering theory on locally symmetric space . In general case for studying scattering theory we need firs spectral decomposition of Hilbert space of square integrable functions locally symmetric spaces of rational rank one is achieved by quotient of symmetric space where G is Lie group and K is maximal compact subgroup by discrete subgroup of Lie group G. By Spectral decomposition theorem we can construct Fourier transform for locally symmetric space and then prove Paley-Wiener Theorem this theorem is main key for scattering machinery.
Keywords:
Automorphic Form ; Fourier Transform ; Locally Symmetric Space ; Scattering Theory ; Payley-Wiener Theorem

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