Author | Plamenevskii, B. A. author |
---|---|

Title | Algebras of Pseudodifferential Operators [electronic resource] / by B. A. Plamenevskii |

Imprint | Dordrecht : Springer Netherlands, 1989 |

Connect to | http://dx.doi.org/10.1007/978-94-009-2364-5 |

Descript | VIII, 292 p. online resource |

CONTENT

1. Integral transforms on a sphere -- 1. The generalized kernels (xy)?ยฑ, (ยฑxy + iO)? -- 2. The operator E(?), its relation with the Fourier and Mellin transform -- 3. The action of E(?) on spherical functions -- 4. Operators related with the transform E(?) -- 5. The spaces Hs(?, Sn-1). The operator E(?) on the spaces Hs(?, Sn-1) -- 6. An analog of the Paley-Wiener theorem for the operator E(?) -- 2. The Fourier transform and convolution operators on spaces with weighted norms -- 1. The spaces H?s(?n) -- 2. The Fourier transform on the spaces Hs?(?n) -- 3. Convolution operator on the spaces Hs?(?n) -- 4. The spaces Hs?(?m,?m-n) -- 5. Transversal operators and special representations -- 6. Estimates for the convolution operator on the spaces H?s(?m, ?m-n) -- 3. Meromorphic pseudodifferential operators -- 1. Canonical meromorphic pseudodifferential operators -- 2. Operations on canonical meromorphic pseudodifferential operators -- 3. General meromorphic pseudodifferential operators -- 4. Traces of meromorphic pseudodifferential operators -- 5. Meromorphic pseudodifferential operators on strongly oscillating functions -- 6. Estimates for meromorphic pseudodifferential operators -- 7. Periodic meromorphic pseudodifferential operators -- 8. Change of variables in meromorphic pseudodifferential operators -- 4. Pseudodifferential operators with discontinuous symbols on manifolds with conical singularities -- 1. Pseudodifferential operators on ?n -- 2. Pseudodifferential operators on a conic manifold -- 3. Pseudodifferential operators on manifolds with conical points -- 4. Algebras generated by pseudodifferential operators of order zero -- 5. The spectrum of a C* -algebra of pseudodifferential operators with discontinuous symbols on a closed manifold -- 1. Results from the theory* of C* -algebras -- 2. The spectrum of a C* -algebra of pseudodifferential operators with discontinuities of the first kind in the symbols on a smooth closed manifold (statement of the main theorem) -- 3. Representations of the algebra $$ \mathfrak{G} $$(?) generated by the operators E(?)-1F(รธ, ?)E(?) -- 4. Representations of an algebra $$ \mathfrak{G} $$(lx) -- 5. Proof of theorem 2.1 -- 6. Ideals in the algebra of pseudodifferential operators with discontinuous symbols -- 7. Spectra of C* -algebras of pseudodifferential operators on a manifold with conical points -- 8. The spectrum of a C* -algebra of pseudodifferential operators with oscillating symbols -- 6. The spectrum of a C* -algebra of pseudodifferential operators on a manifold with boundary -- 1. The algebras $$ \mathfrak{G} $$c(?) -- 2. The algebras $$ \mathfrak{G} $$(?) -- 3. The algebras $$ \mathfrak{G} $$c(l?) -- 4. The algebras $$ \mathfrak{G} $$(l?) -- 5. The spectrum of an algebra of pseudodifferential operators on a manifold with boundary -- Bibliographical sketch -- References

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