Some Classes of Hypoelliptic Pseudodifferential Operators on Closed Manifold

The spectrum of a C* -algebra of pseudodifferential operators with discontinuous symbols on a closed manifold

Algebras of Pseudodifferential Operators ◽

10.1007/978-94-009-2364-5_6 ◽

1989 ◽

pp. 181-233

Author(s):

B. A. Plamenevskii

Keyword(s):

Pseudodifferential Operators ◽

Closed Manifold ◽

C Algebra

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Elliptic pseudodifferential operators in the improved scale of spaces on a closed manifold

Ukrainian Mathematical Journal ◽

10.1007/s11253-007-0056-6 ◽

2007 ◽

Vol 59 (6) ◽

pp. 874-893 ◽

Cited By ~ 15

Author(s):

A. A. Murach

Keyword(s):

Pseudodifferential Operators ◽

Closed Manifold

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Pseudodifferential operators on differential groupoids

Pacific Journal of Mathematics ◽

10.2140/pjm.1999.189.117 ◽

1999 ◽

Vol 189 (1) ◽

pp. 117-152 ◽

Cited By ~ 77

Author(s):

Victor Nistor ◽

Alan Weinstein ◽

Ping Xu

Keyword(s):

Pseudodifferential Operators

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Integrable deformations in the algebra of pseudodifferential operators from a Lie algebraic perspective

Theoretical and Mathematical Physics ◽

10.1007/s11232-013-0011-7 ◽

2013 ◽

Vol 174 (1) ◽

pp. 134-153 ◽

Cited By ~ 13

Author(s):

G. F. Helminck ◽

A. G. Helminck ◽

E. A. Panasenko

Keyword(s):

Pseudodifferential Operators ◽

Integrable Deformations

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Automorphic pseudodifferential operators and vector bundles

Complex Variables Theory and Application An International Journal ◽

10.1080/02781070310001617583 ◽

2003 ◽

Vol 48 (11) ◽

pp. 937-945

Author(s):

Min Ho Lee

Keyword(s):

Vector Bundles ◽

Pseudodifferential Operators

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Subelliptic estimates for certain complexes of pseudodifferential operators

Journal of Differential Equations ◽

10.1016/0022-0396(86)90120-8 ◽

1986 ◽

Vol 61 (2) ◽

pp. 250-267 ◽

Cited By ~ 1

Author(s):

David Hecker ◽

W.J. Sweeney

Keyword(s):

Pseudodifferential Operators

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INFINITE-DIMENSIONAL PSEUDODIFFERENTIAL OPERATORS

Mathematics of the USSR-Izvestiya ◽

10.1070/im1988v031n03abeh001090 ◽

1988 ◽

Vol 31 (3) ◽

pp. 575-601 ◽

Cited By ~ 7

Author(s):

A Yu Khrennikov

Keyword(s):

Pseudodifferential Operators ◽

Infinite Dimensional

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Higher spectral flow and an entire bivariant JLO cocycle

Journal of K-theory K-theory and its Applications to Algebra Geometry and Topology ◽

10.1017/is012008031jkt193 ◽

2012 ◽

Vol 11 (1) ◽

pp. 183-232 ◽

Cited By ~ 5

Author(s):

Moulay-Tahar Benameur ◽

Alan L. Carey

Keyword(s):

Dirac Operator ◽

Chern Character ◽

Dirac Operators ◽

Cyclic Cohomology ◽

Closed Manifold ◽

Spectral Flow ◽

Smooth Functions ◽

Base Manifold ◽

K Theory ◽

Higher Spectral Flow

AbstractFor a single Dirac operator on a closed manifold the cocycle introduced by Jaffe-Lesniewski-Osterwalder [19] (abbreviated here to JLO), is a representative of Connes' Chern character map from the K-theory of the algebra of smooth functions on the manifold to its entire cyclic cohomology. Given a smooth fibration of closed manifolds and a family of generalized Dirac operators along the fibers, we define in this paper an associated bivariant JLO cocycle. We then prove that, for any l ≥ 0, our bivariant JLO cocycle is entire when we endow smoooth functions on the total manifold with the Cl+1 topology and functions on the base manifold with the Cl topology. As a by-product of our theorem, we deduce that the bivariant JLO cocycle is entire for the Fréchet smooth topologies. We then prove that our JLO bivariant cocycle computes the Chern character of the Dai-Zhang higher spectral flow.

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