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Global h Fourier Integral Operators with Complex‐Valued Phase Functions
Author(s) -
Butler J.
Publication year - 2002
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609302001078
Subject(s) - mathematics , fourier transform , fourier integral operator , operator (biology) , kernel (algebra) , gauss , integral transform , pure mathematics , operator theory , algebra over a field , mathematical analysis , chemistry , physics , biochemistry , repressor , quantum mechanics , transcription factor , gene
The author considers globally defined h Fourier integral operators ( h FIO) with complex‐valued phase functions. Symbolic calculus of h FIO is considered and, using a new complex Gauss transform, the composition of h pseudodifferential operators ( h PDO) and h FIO is considered. For a self‐adjoint h PDO A ( h ) and h PDO P ( h ) and Q ( h ) with compactly supported symbols, the results are applied to approximate the kernel of the operatorU P , Q( t ; h ) : = P ( h ) e − i h − 1 t A ( h )Q( h ) * , t ∈ R , h > 0 ,by a single, globally defined h ‐oscillatory integral. 2000 Mathematics Subject Classification 81Q20, 35S30.
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