### Citations

618 | Spectral asymmetry and Riemannian geometry.
- Atiyah, Patodi, et al.
- 1975
(Show Context)
Citation Context ...nal formula ([BG], [D]). In this special case, the asymptotic expansions for the trace of Qe −tP have previously been studied in [BG]; the corresponding trace invariants are important in index theory =-=[APS]-=-. In comparison, the computations required to obtain the heat content asymptotics from the variational formula are rather long and tedious, and the resulting expressions unwieldy; the terms that descr... |

63 |
Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds
- Minakshisundaram, Pleijel
- 1949
(Show Context)
Citation Context ... PB is self-adjoint, the solution of the heat equation can be expressed in terms of the spectral data. This gives a relation between the trace of the heat kernel and the residues of the zeta function =-=[MP]-=-. There exists a similar link between the heat content asymptotics and a suitably modified zeta function. The analysis of [FG] can therefore be extended to obtain an analogous result for the heat cont... |

34 | Gilkey Heat content asymptotics of a Riemannian manifold with boundary,
- Berg, P
- 1994
(Show Context)
Citation Context ...expansion are spectral invariants in the sense that if two manifolds have the same spectrum, then their asymptotic expansion must be equivalent. Recently, new invariants have been computed. See [BD], =-=[BG]-=-, and [DG] for examples. They are known as the heat content. The coefficients of the short-term asymptotic expansion for the heat content have direct applications in theoretical physics [McA]. While t... |

30 | Residues of the eta function for an operator of Dirac type
- Branson, Gilkey
- 1992
(Show Context)
Citation Context ...f|∂M, and B 2 χf =Π−f|∂M ⊕ Π−Qf|∂M.ASYMPTOTIC EXPANSIONS FOR THE HEAT CONTENT 289 The boundary conditions determined by B2 χ can also be obtained from a boundary operator of mixed type. We refer to (=-=[BrG]-=-, Lemma 7) for the proof of: Lemma 4.1. Define Φ ∈ C∞ (End(V )) by Q = γν∇D ν − Φ. Define (i) Bf =Π−f|∂M ⊕ Π+(∇m + γmΦ − 1 2γmγaχ;a)Π+f|∂M. (ii) B2 χf =Π−f|∂M ⊕ Π−Qf|∂M. Then Bf =0if and only if B2 χf... |

20 | Functoriality and heat content asymptotics for operators of Laplace type’, Topol. Methods Nonlinear Anal
- Berg, Desjardins, et al.
- 1993
(Show Context)
Citation Context ...are spectral invariants in the sense that if two manifolds have the same spectrum, then their asymptotic expansion must be equivalent. Recently, new invariants have been computed. See [BD], [BG], and =-=[DG]-=- for examples. They are known as the heat content. The coefficients of the short-term asymptotic expansion for the heat content have direct applications in theoretical physics [McA]. While their study... |

14 |
Heat flow out of regions in
- Berg, Davies
- 1989
(Show Context)
Citation Context ... this expansion are spectral invariants in the sense that if two manifolds have the same spectrum, then their asymptotic expansion must be equivalent. Recently, new invariants have been computed. See =-=[BD]-=-, [BG], and [DG] for examples. They are known as the heat content. The coefficients of the short-term asymptotic expansion for the heat content have direct applications in theoretical physics [McA]. W... |

11 |
Surface energy from heat content asymptotics
- McAvity
- 1993
(Show Context)
Citation Context ...See [BD], [BG], and [DG] for examples. They are known as the heat content. The coefficients of the short-term asymptotic expansion for the heat content have direct applications in theoretical physics =-=[McA]-=-. While their study is parallel in many ways to the study of the classical invariants, their computation often requires 279280 SYLVIE DESJARDINS modifications of the original techniques and, at times... |

8 |
P.: Invariants of the heat equation
- Fegan, Gilkey
- 1985
(Show Context)
Citation Context ...f1,f2,Q,P,B)(t) ≃ ∞∑ n=0 M βn(f1,f2,Q,P,B)t n−q d . The generalized heat operator includes some interesting cases, many of which have been studied previously for the trace invariant. Fegan and Gilkey =-=[FG]-=- have shown that, when ∂M = ∅, the trace invariants associated with the generalized heat operator P a b −tP e , for some a, b > 0, are characterized by the trace invariants of the operator P . ThatAS... |

1 |
Heat content asymptotics, Doctoral Dissertation
- Desjardins
- 1995
(Show Context)
Citation Context ... type Q, it is relatively easy to show that both the trace and the heat content asymptotics can be recovered from those of an operator of Laplace type P = Q 2 by means of a variational formula ([BG], =-=[D]-=-). In this special case, the asymptotic expansions for the trace of Qe −tP have previously been studied in [BG]; the corresponding trace invariants are important in index theory [APS]. In comparison, ... |