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Algebras of pseudodifferential operators on manifolds with singularities. (English. Russian original) Zbl 1065.47045
Dokl. Math. 63, No. 3, 302-305 (2001); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 378, No. 1, 14-17 (2001).
In this Doklady-style paper (i.e., no proofs are given), the authors indicate that in the theory of pseudodifferential operators on manifolds with singularities, the conical case is exceptional in the sense that the set of pseudodifferential operators where coefficients decrease at an exponential rate do not form an algebra.
MSC:
47G30 Pseudodifferential operators
35S99 Pseudodifferential operators and other generalizations of partial differential operators
47L80 Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)
58J40 Pseudodifferential and Fourier integral operators on manifolds
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