Noncommutative Residues, Dixmier’s Trace, and Heat Trace Expansions on Manifolds with Boundary
نویسندگان
چکیده
For manifolds with boundary, we define an extension of Wodzicki’s noncommutative residue to boundary value problems in Boutet de Monvel’s calculus. We show that this residue can be recovered with the help of heat kernel expansions and explore its relation to Dixmier’s trace.
منابع مشابه
The spectral geometry of operators of Dirac and Laplace type
Contents 1 Introduction 2 The geometry of operators of Laplace and Dirac type 3 Heat trace asymptotics for closed manifolds 4 Hearing the shape of a drum 5 Heat trace asymptotics of manifolds with boundary 6 Heat trace asymptotics and index theory 7 Heat content asymptotics 8 Heat content with source terms 9 Time dependent phenomena 10 Spectral boundary conditions 11 Operators which are not of ...
متن کاملOn the Noncommutative Residue and the Heat Trace Expansion on Conic Manifolds
Given a cone pseudodifferential operator P we give a full asymptotic expansion as t → 0 of the trace TrPe, where A is an elliptic cone differential operator for which the resolvent exists on a suitable region of the complex plane. Our expansion contains log t and new (log t) terms whose coefficients are given explicitly by means of residue traces. Cone operators are contained in some natural al...
متن کاملTrace Expansions and the Noncommutative Residue for Manifolds with Boundary
For a pseudodifferential boundary operator A of order ν ∈ Z and class 0 (in the Boutet de Monvel calculus) on a compact n-dimensional manifold with boundary, we consider the function Tr(AB−s), where B is an auxiliary system formed of the Dirichlet realization of a second order strongly elliptic differential operator and an elliptic operator on the boundary. We prove that Tr(AB−s) has a meromorp...
متن کاملThe Local and Global Parts of the Basic Zeta Coefficient for Operators on Manifolds with Boundary
For operators on a compact manifold X with boundary ∂X, the basic zeta coefficient C0(B, P1,T ) is the regular value at s = 0 of the zeta function Tr(BP −s 1,T ), where B = P+ +G is a pseudodifferential boundary operator (in the Boutet de Monvel calculus) — for example the solution operator of a classical elliptic problem — and P1,T is a realization of an elliptic differential operator P1, havi...
متن کاملParametrized Pseudodifferential Operators and Geometric Invariants
This is based on joint work with R. T. Seeley. The introduction presents the problem of parameter-dependent calculi for do's and the question of trace asymptotics for Atiyah-Patodi-Singer operators. Chapter 2 establishes relations between the three operator functions: resolvent, heat operator and power operator (zeta function). Chapter 3 explains our parameter-dependent do calculus with weak po...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008