Elliptic operators in even subspaces
Sbornik. Mathematics, Tome 190 (1999) no. 8, pp. 1195-1228 Cet article a éte moissonné depuis la source Math-Net.Ru

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An elliptic theory is constructed for operators acting in subspaces defined in terms of even pseudodifferential projections. Index formulae are obtained for operators on compact manifolds without boundary and for general boundary-value problems. A connection with Gilkey's theory of $\eta$-invariants is established.
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A. Yu. Savin; B. Yu. Sternin. Elliptic operators in even subspaces. Sbornik. Mathematics, Tome 190 (1999) no. 8, pp. 1195-1228. http://geodesic.mathdoc.fr/item/SM_1999_190_8_a4/

[1] Atiyah M. F., Bott R., “The index problem for manifolds with boundary”, Differ. Analysis, Bombay Colloquium, Oxford Univ. Press, Oxford, 1964, 175–186 | MR

[2] Sternin B. Yu., Shatalov V. E., Shultse B.-V., “Ob obschikh kraevykh zadachakh dlya ellipticheskikh uravnenii”, Matem. sb., 189:10 (1998), 145–160 | MR | Zbl

[3] Atiyah M. F., Patodi V. K., Singer I. M., “Spectral asymmetry and Riemannian geometry, I”, Math. Proc. Cambridge Philos. Soc., 77 (1975), 43–69 | DOI | MR | Zbl

[4] Savin A. Yu., Sternin B. Yu., Shultse B.-V., “Ob invariantnykh formulakh indeksa dlya spektralnykh kraevykh zadach”, Differents. uravneniya, 35:5 (1999), 705–714 | MR | Zbl

[5] Savin A. Yu., “Ob operatorakh, dopuskayuschikh razbienie formuly indeksa spektralnykh kraevykh zadach”, Dokl. RAN (to appear)

[6] Hörmander L., The analysis of linear partial differential operators, V. III, Springer-Verlag, Berlin, 1985 | MR

[7] Nazaikinskii V. E., Sternin B. Yu., Shatalov V. E., Shultse B.-V., “Spektralnye kraevye zadachi i ellipticheskie uravneniya na mnogoobraziyakh s osobennostyami”, Differents. uravneniya, 34:5 (1998), 695–708 | MR | Zbl

[8] Gilkey P. B., “The eta invariant of even order operators”, Differential geometry, Proc. 3rd Int. Symp. (Peniscola, Spain, 1988), Lecture Notes in Math., 1410, 1989, 202–211 | MR | Zbl

[9] Birman M. S., Solomyak M. Z., “O podprostranstvakh, dopuskayuschikh psevdodifferentsialnyi proektor”, Vestn. LGU. Ser. matem., mekh., astronom., 1982, no. 1, 18–25 | MR | Zbl

[10] Melrose R. B., Piazza P., “Families of Dirac operators, boundaries and the $B$-calculus”, J. Differential Geom., 46:1 (1997), 99–180 | MR | Zbl

[11] Wojciechowski K., “A note on the space of pseudodifferential projections with the same principal symbol”, J. Operator Theory, 15:2 (1986), 207–216 | MR | Zbl

[12] Atiyah M. F., Patodi V. K., Singer I. M., “Spectral asymmetry and Riemannian geometry, III”, Math. Proc. Cambridge Philos. Soc., 79 (1976), 71–99 | DOI | MR | Zbl

[13] Dai X., Zhang W., “Splitting of the family index”, Comm. Math. Phys., 182:2 (1996), 303–318 | DOI | MR | Zbl

[14] Atiyah M. F., Bott R., Patodi V. K., “On the heat equation and the index theorem”, Invent. Math., 19 (1973), 279–330 | DOI | MR | Zbl

[15] Atiyah M. F., Singer I. M., “The index of elliptic operators, I”, Ann. of Math. (2), 87 (1968), 484–530; | DOI | MR | Zbl

[16] Rempel S., Schulze B.-W., Index theory of elliptic boundary problems, Akademie-Verlag, Berlin, 1982 | MR

[17] Agranovich M. S., Vishik M. I., “Ellipticheskie zadachi s parametrom i parabolicheskie zadachi obschego vida”, UMN, 19:3 (1964), 53–161 | MR | Zbl

[18] Gilkey P. B., “The eta invariant for even dimensional $\textPIN_c$ manifolds”, Adv. Math., 58 (1985), 243–284 | DOI | MR | Zbl