Download Analysis, Geometry and Topology of Elliptic Operators: by Matthias Lesch, Bernhelm Booβ-Bavnbek, Slawomir Klimek, PDF

By Matthias Lesch, Bernhelm Booβ-Bavnbek, Slawomir Klimek, Weiping Zhang

Smooth idea of elliptic operators, or just elliptic conception, has been formed through the Atiyah-Singer Index Theorem created forty years in the past. Reviewing elliptic thought over a large diversity, 32 major scientists from 14 diverse international locations current fresh advancements in topology; warmth kernel options; spectral invariants and slicing and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics.The first of its variety, this quantity is splendid to graduate scholars and researchers attracted to cautious expositions of newly-evolved achievements and views in elliptic thought. The contributions are in response to lectures awarded at a workshop acknowledging Krzysztof P Wojciechowski's paintings within the conception of elliptic operators.

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Extra info for Analysis, Geometry and Topology of Elliptic Operators: Papers in Honor of Krzysztof P Wojciechowski

Example text

Finally we assume the following expression of Ax over W Uy Z, d2 Ax|wuyZ = - - j - ^ + Ay (5) where Ay is a Laplace type operator over Y. As before, we impose the Dirichlet boundary conditions for the restrictions of A x to A^ and Z and denote by Ajv, A% the resulting operators. Then the relative £-function for (Ax, Az) is defined by C(s, A x , A Z ) := | ^ y ( £ +£ )ts~l T r ( e - ' A * - e~^)dt. Here the integral fQ • dt has a meromorphic extension from 5Rs S> 0 to C and the integral Jx • dt has a meromorphic extension from Ks

References . 1. M. F . Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry I, Math. Proc. Cambridge Philos. Soc. 77 (1975), 43-69. 2. M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry II, Math. Proc. Cambridge Philos. Soc. 78 (1975), 405432. 3. , Spectral asymmetry and Riemannian geometry III, Math. Proc. Cambridge Philos. Soc. 79 (1976), 71-99. 4. B. Boofl and K. P. Wojciechowski, Desuspension and splitting elliptic symbols I, Ann.

Mazzeo, and R. B. Melrose, Analytic surgery and the accumulation of eigenvalues, Comm. Anal. Geom. 3 (1995), 115-222. 13. A. Hassell and S. Zelditch, Determinants of Laplacians in exterior domains, IMRN 18 (1999), 971-1004. Gluing formulae of spectral invariants and Cauchy data spaces 37 14. P. Kirk and M. Lesch, The eta invariant, Maslov index, and spectral flow for Dirac-type operators on manifolds with boundary, Forum Math. 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.

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