New PDF release: Analysis, Geometry And Topology of Elliptic Operators:

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

ISBN-10: 9812568050

ISBN-13: 9789812568052

ISBN-10: 9812773606

ISBN-13: 9789812773609

Smooth conception of elliptic operators, or just elliptic concept, has been formed through the Atiyah-Singer Index Theorem created forty years in the past. Reviewing elliptic concept over a large variety, 32 best scientists from 14 diverse international locations current contemporary advancements in topology; warmth kernel ideas; spectral invariants and slicing and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics. the 1st of its type, this quantity is preferrred to graduate scholars and researchers drawn 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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Additional info for Analysis, Geometry And Topology of Elliptic Operators: Papers in Honor of Krysztof P. Wojciechowski

Sample text

26 Jinsung Park 2. Gluing formula of the ^-regularized determinant of a Laplace type operator In this section, we review the gluing formula of the ^-regularized determinant of a Laplace type operator. This type of formula was first proved by Burghelea, Friedlander and Kappeler (BFK) in [7] where they call this a Mayer-Vietoris type formula. Although their formula holds for a more general situation, that is, more general differential operators and general local elliptic boundary conditions, here we just restrict our discussion to a Laplace type operator and the Dirichlet boundary condition.

For 7T : T*X -> X and u G C°°(£), let u A G C°°(n*E) be denned (where x = TT(0 and £ e T*X) by u A (£) := /" e-*Wl>(\v\)Tf X, of the bump function a(a;, •) times u(-) in a neighborhood of a;, and UA\T*X is the Fourier transform of this "pull-back" of a(x,-)u(-).

Let TTE '• E —+ X and np : F —> X be complex hermitian vector Behavior of the analytic index under nontrivial embedding 43 bundles equipped with hermitian connections VE : C°°(E) —• C°°(T*X E) and V F : C°°(F) -* C°°(T*X ® F), where C°°{E) denotes the space of (smooth) sections of -KE '• E —* X. For x,y £ X, with d(x,y) < p, let T^ y : Ey —* Ex denote parallel translation relative to V E along the unique geodesic from y to x with minimal length d(x,y). Let i/> : [0, oo) —> [0,1] be smooth, with ip(r) = 1 for r G [0,p/3] and tp(r) — 0 for r G [2p/3, oo].

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Analysis, Geometry And Topology of Elliptic Operators: Papers in Honor of Krysztof P. Wojciechowski by Matthias Lesch, Bernhelm Booss-Bavnbek, Slawomir Klimek, Weiping Zhang


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