Journal
JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS
Volume 6, Issue 1, Pages 1-9Publisher
SPRINGER BASEL AG
DOI: 10.1007/s11868-015-0108-x
Keywords
Pseudo-differential operators; Quantization; Broken symmetry; Finite abelian groups; Characters; Dual groups; Plancherel's formula; Fourier inversion formula; Traces; Matrices; L-2-boundedness; Self-adjointness; Invertible elements; Permanents; Determinants; Spectral invariance
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We give the basic theory of pseudo-differential operators on finite abelian groups. In the case of a group with two elements, we give a criterion for invertibility of these operators and we also give a solution of the spectral invariance problem for these operators.
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