Functional determinant (English Wikipedia)

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(Branson 1993); (Osgood, Phillips & Sarnak 1988) Branson, Thomas P. (1993), The functional determinant, Lecture Notes Series, vol. 4, Seoul: Seoul National University Research Institute of Mathematics Global Analysis Research Center, MR 1325463 Osgood, B.; Phillips, R.; Sarnak, Peter (1988), "Extremals of determinants of Laplacians", Journal of Functional Analysis, 80 (1): 148–211, doi:10.1016/0022-1236(88)90070-5, ISSN 0022-1236, MR 0960228
See Osgood, Phillips & Sarnak (1988). For a more general definition in terms of the spectral function, see Hörmander (1968) or Shubin (1987). Osgood, B.; Phillips, R.; Sarnak, Peter (1988), "Extremals of determinants of Laplacians", Journal of Functional Analysis, 80 (1): 148–211, doi:10.1016/0022-1236(88)90070-5, ISSN 0022-1236, MR 0960228 Hörmander, Lars (1968), "The spectral function of an elliptic operator", Acta Mathematica, 121: 193–218, doi:10.1007/BF02391913, ISSN 0001-5962, MR 0609014 Shubin, M. A. (1987), Pseudodifferential operators and spectral theory, Springer Series in Soviet Mathematics, Berlin, New York: Springer-Verlag, ISBN 978-3-540-13621-7, MR 0883081
For the case of the generalized Laplacian, as well as regularity at zero, see Berline, Getzler & Vergne (2004, Proposition 9.35). For the general case of an elliptic pseudodifferential operator, see Seeley (1967). Seeley, R. T. (1967), "Complex powers of an elliptic operator", Singular Integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966), Providence, R.I.: American Mathematical Society, pp. 288–307, MR 0237943

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(Branson 1993); (Osgood, Phillips & Sarnak 1988) Branson, Thomas P. (1993), The functional determinant, Lecture Notes Series, vol. 4, Seoul: Seoul National University Research Institute of Mathematics Global Analysis Research Center, MR 1325463 Osgood, B.; Phillips, R.; Sarnak, Peter (1988), "Extremals of determinants of Laplacians", Journal of Functional Analysis, 80 (1): 148–211, doi:10.1016/0022-1236(88)90070-5, ISSN 0022-1236, MR 0960228
See Osgood, Phillips & Sarnak (1988). For a more general definition in terms of the spectral function, see Hörmander (1968) or Shubin (1987). Osgood, B.; Phillips, R.; Sarnak, Peter (1988), "Extremals of determinants of Laplacians", Journal of Functional Analysis, 80 (1): 148–211, doi:10.1016/0022-1236(88)90070-5, ISSN 0022-1236, MR 0960228 Hörmander, Lars (1968), "The spectral function of an elliptic operator", Acta Mathematica, 121: 193–218, doi:10.1007/BF02391913, ISSN 0001-5962, MR 0609014 Shubin, M. A. (1987), Pseudodifferential operators and spectral theory, Springer Series in Soviet Mathematics, Berlin, New York: Springer-Verlag, ISBN 978-3-540-13621-7, MR 0883081

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(Branson 1993); (Osgood, Phillips & Sarnak 1988) Branson, Thomas P. (1993), The functional determinant, Lecture Notes Series, vol. 4, Seoul: Seoul National University Research Institute of Mathematics Global Analysis Research Center, MR 1325463 Osgood, B.; Phillips, R.; Sarnak, Peter (1988), "Extremals of determinants of Laplacians", Journal of Functional Analysis, 80 (1): 148–211, doi:10.1016/0022-1236(88)90070-5, ISSN 0022-1236, MR 0960228
See Osgood, Phillips & Sarnak (1988). For a more general definition in terms of the spectral function, see Hörmander (1968) or Shubin (1987). Osgood, B.; Phillips, R.; Sarnak, Peter (1988), "Extremals of determinants of Laplacians", Journal of Functional Analysis, 80 (1): 148–211, doi:10.1016/0022-1236(88)90070-5, ISSN 0022-1236, MR 0960228 Hörmander, Lars (1968), "The spectral function of an elliptic operator", Acta Mathematica, 121: 193–218, doi:10.1007/BF02391913, ISSN 0001-5962, MR 0609014 Shubin, M. A. (1987), Pseudodifferential operators and spectral theory, Springer Series in Soviet Mathematics, Berlin, New York: Springer-Verlag, ISBN 978-3-540-13621-7, MR 0883081