The spectrum of an algebra of pseudodifferential operators with piecewise smooth symbols

The authors study the spectrum of a $C^*$-algebra of pseudodifferential operators whose symbols have discontinuities along submanifolds (the supports of the discontinuities) intersecting at nonzero angles. All (up to equivalence) irreducible representations of such algebras are enumerated, a realization of these representations is indicated, and the spectral topology is described.
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