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26 April 2024 |
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Guillemin Transform and Toeplitz Representations for Operators on Singular Manifolds | | V. Nazaikinskii
; G. Rozenblum
; A. Savin
; B. Sternin
; | | Date: |
14 Mar 2005 | | Journal: | "Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds", ed. Bernhelm Booss-Bavnbek and Krzysztof P. Wojciechowski, Contemp.Math., 366, 2005, 281-306 | | Subject: | Analysis of PDEs; Functional Analysis; Operator Algebras MSC-class: 46L80 (Primary) 58J20 46L87 58J40 (Secondary) | math.AP math.FA math.OA | | Abstract: | An approach to the construction of index formulas for elliptic operators on singular manifolds is suggested on the basis of K-theory of algebras and cyclic cohomology. The equivalence of Toeplitz and pseudodifferential quantizations, well known in the case of smooth closed manifolds, is extended to the case of manifolds with conical singularities. We describe a general construction that permits one, for a given Toeplitz quantization of a C^*-algebra, to obtain a new equivalent Toeplitz quantization provided that a resolution of the projection determining the original quantization is given. | | Source: | arXiv, math.AP/0503267 | | Services: | Forum | Review | PDF | Favorites | |
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