By Matthias Lesch, Bernhelm Booss-Bavnbek, Slawomir Klimek, Weiping Zhang
Smooth idea of elliptic operators, or just elliptic idea, has been formed via the Atiyah-Singer Index Theorem created forty years in the past. Reviewing elliptic concept over a huge variety, 32 major scientists from 14 assorted international locations current contemporary advancements in topology; warmth kernel concepts; spectral invariants and slicing and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics. the 1st of its style, this quantity is superb to graduate scholars and researchers attracted to cautious expositions of newly-evolved achievements and views in elliptic idea. The contributions are in accordance with lectures provided at a workshop acknowledging Krzysztof P Wojciechowski's paintings within the idea of elliptic operators.
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Additional resources for Analysis, Geometry And Topology of Elliptic Operators: Papers in Honor of Krysztof P. Wojciechowski
Anal. 136 (1996), 269-293. 16. M. Lesch and K. P. Wojciechowski, On the rj-invariant of generalized AtiyahPatodi-Singer boundary value problems, Illinois J. Math. 40 (1996), 30-46. 17. P. Loya and J. Park, On the gluing problem for the spectral invariants of dirac operators, To appear. 18. W. Miiller, Eta invariants and manifolds with boundary, J. Differential Geom. 40 (1994), 311-377. 19. J. Park and K. P. Wojciechowski, Adiabatic decomposition of the £ determinant of the Dirac Laplacian I. The case of invertible tangential operator, Comm.
Blaine Lawson and Marie-Louise Michelsohn [6, p. 188] point out the possible desirability of defining pseudo-differential operators with a global symbol. In essence, here we are exploring this possibility. We find that some of the difficulties are softened. In particular, the lifting a pseudo-differential operator to an invariant one in the proof of the twisted multiplication formula is made easier, since the global symbol can be lifted by means of a connection. Moreover the thorny problem of forming suitable products of individual pseudo-differential operators with identity operators over product manifolds (see [6, p.
16 (2004), 553-629. 15. Y. Lee, Burghelea-Friedlander-Kappeler's gluing formula for the zetadeterminant and its applications to the adiabatic decompositions of the zetadeterminant and the analytic torsion, Trans. Amer. Math. Soc. 355, no. 10 (2003), 4093-4110. 16. P. Loya and J. Park, Decomposition of the zeta-determinant for the Laplacian on manifolds with cylindrical end, Illinois J. Math. 48, no. 4 (2004), 1279-1303. 17. P. Loya and J. Park, On the gluing problem for the spectral invariants of Dirac operators, Adv.
Analysis, Geometry And Topology of Elliptic Operators: Papers in Honor of Krysztof P. Wojciechowski by Matthias Lesch, Bernhelm Booss-Bavnbek, Slawomir Klimek, Weiping Zhang