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A Time Dependent Scattering Theory for a Class of Simply Characteristic Operators with Short Range Local Potentials
Author(s) -
Muthuramalingam Pl.
Publication year - 1985
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-32.2.259
Subject(s) - mathematics , eigenvalues and eigenvectors , singularity , completeness (order theory) , operator (biology) , range (aeronautics) , spectrum (functional analysis) , class (philosophy) , polynomial , pure mathematics , mathematical physics , mathematical analysis , combinatorics , discrete mathematics , physics , quantum mechanics , computer science , chemistry , artificial intelligence , composite material , biochemistry , materials science , repressor , transcription factor , gene
Let H = H 0 + W S (Q), where (i) H 0 = h 0 ( P ), (ii) h 0 is a real‐valued simply characteristic polynomial on R n with {0} = { n:h 0 (ξ + tη ) = h 0 (ξ) for all ξ and real t } and (iii) W s is a real‐valued short range potential with some local singularity. Using time dependent methods we prove, for the operator H (a) the absence of singular continuous spectrum, (b) asymptotic completeness and (c) accumulation of eigenvalues only at the critical values of the symbol h 0 . The class H 0 is precisely that for which a stationary theory is developed in [ 6 ].