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Volumn 7, Issue 1, 2004, Pages 9-46

Heat kernel asymptotics of Zaremba boundary value problem

Author keywords

Boundary value problem; Heat kernel; Spectral asymptotics; Spectral geometry

Indexed keywords


EID: 1842481657     PISSN: 13850172     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:MPAG.0000022837.63824.4c     Document Type: Article
Times cited : (12)

References (45)
  • 1
    • 0010083733 scopus 로고    scopus 로고
    • A covariant technique for the calculation of the one-loop effective action
    • Avramidi, I. G.: A covariant technique for the calculation of the one-loop effective action, Nuclear Phys. B 355 (1991), 712-754. Erratum: Nuclear Phys. B 509 (1998), 557-558.
    • (1991) Nuclear Phys. B , vol.355 , pp. 712-754
    • Avramidi, I.G.1
  • 2
    • 0010083733 scopus 로고    scopus 로고
    • Erratum
    • Avramidi, I. G.: A covariant technique for the calculation of the one-loop effective action, Nuclear Phys. B 355 (1991), 712-754. Erratum: Nuclear Phys. B 509 (1998),
    • (1998) Nuclear Phys. B , vol.509 , pp. 557-558
  • 3
    • 0008983525 scopus 로고
    • A method for calculating the heat kernel for manifolds with boundary
    • Russian
    • Avramidi, I. G.: A method for calculating the heat kernel for manifolds with boundary, Yadernaya Fiz. 56 (1993), 245-252, [Russian]; Phys. Atomic Nuclei 56 (1993), 138-142 [English].
    • (1993) Yadernaya Fiz. , vol.56 , pp. 245-252
    • Avramidi, I.G.1
  • 4
    • 3543112778 scopus 로고
    • English
    • Avramidi, I. G.: A method for calculating the heat kernel for manifolds with boundary, Yadernaya Fiz. 56 (1993), 245-252, [Russian]; Phys. Atomic Nuclei 56 (1993), 138-142 [English].
    • (1993) Phys. Atomic Nuclei , vol.56 , pp. 138-142
  • 5
    • 0032367544 scopus 로고    scopus 로고
    • Green functions of higher-order differential operators
    • Avramidi, I. G.: Green functions of higher-order differential operators, J. Math. Phys. 39 (1998), 2889-2909.
    • (1998) J. Math. Phys. , vol.39 , pp. 2889-2909
    • Avramidi, I.G.1
  • 6
    • 0033446602 scopus 로고    scopus 로고
    • Covariant techniques for computation of the heat kernel
    • Avramidi, I. G.: Covariant techniques for computation of the heat kernel, Rev. Math. Phys. 11 (1999), 947-980.
    • (1999) Rev. Math. Phys. , vol.11 , pp. 947-980
    • Avramidi, I.G.1
  • 7
    • 0003305541 scopus 로고    scopus 로고
    • Heat kernel asymptotics of non-smooth boundary value problem, New Mexico Tech., 1999
    • M. van den Berg and V. Liskevich (eds), Abstracts of Int. Conf., University of Bristol, Bristol, U.K., July 10-15
    • Avramidi, I. G.: Heat kernel asymptotics of non-smooth boundary value problem, New Mexico Tech., 1999; In: M. van den Berg and V. Liskevich (eds), Workshop on Spectral Geometry, Abstracts of Int. Conf., University of Bristol, Bristol, U.K., July 10-15, 2000.
    • (2000) Workshop on Spectral Geometry
    • Avramidi, I.G.1
  • 8
    • 0032391433 scopus 로고    scopus 로고
    • Lack of strong ellipticity in Euclidean quantum gravity
    • Avramidi, I. G. and Esposito, G.: Lack of strong ellipticity in Euclidean quantum gravity, Classical Quantum Gravity 15, (1998), 1141-1152.
    • (1998) Classical Quantum Gravity , vol.15 , pp. 1141-1152
    • Avramidi, I.G.1    Esposito, G.2
  • 9
    • 0033514095 scopus 로고    scopus 로고
    • Gauge theories on manifolds with boundary
    • Avramidi, I. G. and Esposito, G.: Gauge theories on manifolds with boundary, Comm. Math. Phys. 200 (1999), 495-543.
    • (1999) Comm. Math. Phys. , vol.200 , pp. 495-543
    • Avramidi, I.G.1    Esposito, G.2
  • 10
    • 0345573223 scopus 로고    scopus 로고
    • Heat kernel asymptotics of the Gilkey-Smith boundary value problem
    • V. Alexiades and G. Siopsis (eds) Stud. Adv. Math. 13, Amer. Math. Soc. and International Press
    • Avramidi, I. G. and Esposito, G.: Heat kernel asymptotics of the Gilkey-Smith boundary value problem, In: V. Alexiades and G. Siopsis (eds), Trends in Mathematical Physics, Stud. Adv. Math. 13, Amer. Math. Soc. and International Press, 1999, pp. 15-34.
    • (1999) Trends in Mathematical Physics , pp. 15-34
    • Avramidi, I.G.1    Esposito, G.2
  • 11
    • 0000836662 scopus 로고    scopus 로고
    • Algorithms for the calculation of the heat kernel coefficients
    • M. Bordag (ed.), Teubner-Texte Phys. 30, Teubner, Stuttgart
    • Avramidi, I. G. and Schimming, R.: Algorithms for the calculation of the heat kernel coefficients, In: M. Bordag (ed.), Quantum Field Theory under the Influence of External Conditions, Teubner-Texte Phys. 30, Teubner, Stuttgart, 1996, pp. 150-162.
    • (1996) Quantum Field Theory under the Influence of External Conditions , pp. 150-162
    • Avramidi, I.G.1    Schimming, R.2
  • 14
    • 84953832735 scopus 로고
    • The asymptotics of the Laplacian on a manifold with boundary
    • Branson, T. and Gilkey, P. B.: The asymptotics of the Laplacian on a manifold with boundary, Comm. Partial Differential Equations 15 (1990), 245-272.
    • (1990) Comm. Partial Differential Equations , vol.15 , pp. 245-272
    • Branson, T.1    Gilkey, P.B.2
  • 16
    • 0000954557 scopus 로고
    • Regular singular asymptotics
    • Brüning, J. and Seeley, R.: Regular singular asymptotics, Adv. in Math. 58 (1985), 133-148.
    • (1985) Adv. in Math. , vol.58 , pp. 133-148
    • Brüning, J.1    Seeley, R.2
  • 17
    • 0000473131 scopus 로고
    • The expansion of the resolvent near a singular stratum of conical type
    • Brüning, J. and Seeley, R,. T.: The expansion of the resolvent near a singular stratum of conical type, J. Funct. Anal. 95 (1991), 255-290.
    • (1991) J. Funct. Anal. , vol.95 , pp. 255-290
    • Brüning, J.1    Seeley, R.T.2
  • 18
    • 0013469059 scopus 로고
    • The heat equation with singular coefficients I
    • Callias, C.: The heat equation with singular coefficients I, Comm. Math. Phys. 88 (1983), 357-385.
    • (1983) Comm. Math. Phys. , vol.88 , pp. 357-385
    • Callias, C.1
  • 19
    • 0001679198 scopus 로고
    • On the spectral geometry of spaces with cone-like singularities
    • Cheeger, J.: On the spectral geometry of spaces with cone-like singularities, Proc. Nat. Acad. Sci. U.S.A. 76 (1979), 2103-2106.
    • (1979) Proc. Nat. Acad. Sci. U.S.A. , vol.76 , pp. 2103-2106
    • Cheeger, J.1
  • 20
    • 84972545480 scopus 로고
    • Spectral geometry of singular Riemannian spaces
    • Cheeger, J.: Spectral geometry of singular Riemannian spaces, J. Differential Geom. 18 (1983), 575-657.
    • (1983) J. Differential Geom. , vol.18 , pp. 575-657
    • Cheeger, J.1
  • 21
    • 0002442079 scopus 로고
    • The spacetime approach to quantum field theory
    • B. S. De Witt and R. Stora (eds), North-Holland, Amsterdam
    • De Witt, B. S.: The Spacetime Approach to Quantum Field Theory, In: B. S. De Witt and R. Stora (eds), Relativity, Groups and Topology II, North-Holland, Amsterdam, 1984, pp. 383-738.
    • (1984) Relativity, Groups and Topology II , pp. 383-738
    • De Witt, B.S.1
  • 22
    • 0007056147 scopus 로고    scopus 로고
    • University of Manchester, hepth/0007127
    • Dowker, J. S.: The N ∪ D problem, University of Manchester, 2000, hepth/0007127.
    • (2000) The N ∪ D Problem
    • Dowker, J.S.1
  • 23
    • 0035535903 scopus 로고    scopus 로고
    • On properties of the asymptotic expansion of the heat trace for the N/D problem
    • Dowker, J. S., Gilkey, P. B. and Kirsten, K.: On properties of the asymptotic expansion of the heat trace for the N/D problem, Internat. J. Math. 12 (2001), 505-517.
    • (2001) Internat. J. Math. , vol.12 , pp. 505-517
    • Dowker, J.S.1    Gilkey, P.B.2    Kirsten, K.3
  • 24
    • 0039054333 scopus 로고    scopus 로고
    • Heat-kernel coefficients for oblique boundary conditions
    • Dowker, J. S. and Kirsten, K.: Heat-kernel coefficients for oblique boundary conditions, Classical Quantum Gravity 14 (1997), L169-L175.
    • (1997) Classical Quantum Gravity , vol.14
    • Dowker, J.S.1    Kirsten, K.2
  • 25
    • 0033148826 scopus 로고    scopus 로고
    • 3/2 heat-kernel coefficient for oblique boundary conditions
    • 3/2 heat-kernel coefficient for oblique boundary conditions, Classical Quantum Gravity 16 (1999), 1917-1936.
    • (1999) Classical Quantum Gravity , vol.16 , pp. 1917-1936
    • Dowker, J.S.1    Kirsten, K.2
  • 26
    • 0033239517 scopus 로고    scopus 로고
    • Heat kernel coefficients for Chern-Simons boundary conditions in QED
    • Elizalde, E. and Vassilevich, D. V.: Heat Kernel Coefficients for Chern-Simons Boundary Conditions in QED, Classical Quantum Gravity 16 (1999), 813-823.
    • (1999) Classical Quantum Gravity , vol.16 , pp. 813-823
    • Elizalde, E.1    Vassilevich, D.V.2
  • 28
    • 0000321173 scopus 로고
    • Asymptotic formulas for the eigenvalues of the Laplace operator in the case of a polyhedron
    • Fedosov, B. V.: Asymptotic formulas for the eigenvalues of the Laplace operator in the case of a polyhedron, Soviet Math. Dokl. 5 (1964), 988-990.
    • (1964) Soviet Math. Dokl. , vol.5 , pp. 988-990
    • Fedosov, B.V.1
  • 30
    • 84990623241 scopus 로고
    • The eta invariant for a class of elliptic boundary value problems
    • Gilkey, P. B. and Smith, L.: The eta invariant for a class of elliptic boundary value problems, Comm. Pure Appl. Math. 36 (1983), 85-132.
    • (1983) Comm. Pure Appl. Math. , vol.36 , pp. 85-132
    • Gilkey, P.B.1    Smith, L.2
  • 31
    • 84972530309 scopus 로고
    • The twisted index theorem for manifolds with boundary
    • Gilkey, P. B. and Smith, L.: The twisted index theorem for manifolds with boundary, J. Differential Geom. 18 (1983), 393-344.
    • (1983) J. Differential Geom. , vol.18 , pp. 393-344
    • Gilkey, P.B.1    Smith, L.2
  • 33
    • 0242590105 scopus 로고
    • Properties of normal boundary value problems for elliptic even-order systems
    • Grubb, G.: Properties of normal boundary value problems for elliptic even-order systems, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 1 (1974), 1-61.
    • (1974) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.1 , pp. 1-61
    • Grubb, G.1
  • 35
    • 0013502399 scopus 로고    scopus 로고
    • Asymptotics of the parabolic Green function for an elliptic operator on a manifold with conical points
    • Karol', A. L: Asymptotics of the parabolic Green function for an elliptic operator on a manifold with conical points, Math. Notes 63(1-2) (1998), 25-32.
    • (1998) Math. Notes , vol.63 , Issue.1-2 , pp. 25-32
    • Karol', A.L.1
  • 36
    • 0039065134 scopus 로고    scopus 로고
    • 5 heat kernel coefficient on a manifold with boundary
    • 5 heat kernel coefficient on a manifold with boundary, Classical Quantum Gravity 15 (1998), L5-L12.
    • (1998) Classical Quantum Gravity , vol.15
    • Kirsten, K.1
  • 38
    • 0001636832 scopus 로고
    • Asymptotic expansion of the heat kernel for generalized boundary conditions
    • McAvity, D. M. and Osborn, H.: Asymptotic expansion of the heat kernel for generalized boundary conditions, Classical Quantum Gravity 8 (1991), 1445-1454.
    • (1991) Classical Quantum Gravity , vol.8 , pp. 1445-1454
    • McAvity, D.M.1    Osborn, H.2
  • 39
    • 0001842304 scopus 로고    scopus 로고
    • Heat kernel asymptotics on manifolds with conic singularities
    • Mooers, E. A.: Heat kernel asymptotics on manifolds with conic singularities, J. Anal. Math. 78 (1999), 1-36.
    • (1999) J. Anal. Math. , vol.78 , pp. 1-36
    • Mooers, E.A.1
  • 41
    • 0001441798 scopus 로고
    • The resolvent of an elliptic boundary value problem
    • Seeley, R. T.: The resolvent of an elliptic boundary value problem, Amer. J. Math. 91 (1969), 963-983.
    • (1969) Amer. J. Math. , vol.91 , pp. 963-983
    • Seeley, R.T.1
  • 42
    • 0036956655 scopus 로고    scopus 로고
    • Trace expansions for the Zaremba problem
    • Seeley, R. T.: Trace Expansions for the Zaremba Problem, Comm. Partial Differential Equations 27 (2002), 2403-2421.
    • (2002) Comm. Partial Differential Equations , vol.27 , pp. 2403-2421
    • Seeley, R.T.1
  • 45
    • 0032367484 scopus 로고    scopus 로고
    • Index free heat kernel coefficients
    • van de Ven, A. E. M.: Index free heat kernel coefficients, Classical Quantum Gravity 15 (1998), 2311-2344.
    • (1998) Classical Quantum Gravity , vol.15 , pp. 2311-2344
    • Van De Ven, A.E.M.1


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