Abstract:
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 η-invariants is established.
\Bibitem{SavSte99}
\by A.~Yu.~Savin, B.~Yu.~Sternin
\paper Elliptic operators in even subspaces
\jour Sb. Math.
\yr 1999
\vol 190
\issue 8
\pages 1195--1228
\mathnet{http://mi.mathnet.ru/eng/sm423}
\crossref{https://doi.org/10.1070/sm1999v190n08ABEH000423}
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https://www.mathnet.ru/eng/sm423
https://doi.org/10.1070/sm1999v190n08ABEH000423
https://www.mathnet.ru/eng/sm/v190/i8/p125
This publication is cited in the following 17 articles:
A. Yu. Savin, “On Homotopy Classification of Elliptic Problems with Contractions and K-Groups of Corresponding C*-Algebras”, J Math Sci, 260:4 (2022), 555
A. Yu. Savin, “O gomotopicheskoi klassifikatsii ellipticheskikh zadach so szhatiyami i K-gruppakh sootvetstvuyuschikh C∗-algebr”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 64, no. 1, Rossiiskii universitet druzhby narodov, M., 2018, 164–179
Savin A. Sternin B., “Index of Elliptic Operators For Diffeomorphisms of Manifolds”, J. Noncommutative Geom., 8:3 (2014), 695–734
Jörg Seiler, “Ellipticity in pseudodifferential algebras of Toeplitz type”, Journal of Functional Analysis, 2012
A. Yu. Savin, “On the Index of Nonlocal Elliptic Operators Corresponding to a Nonisometric Diffeomorphism”, Math. Notes, 90:5 (2011), 701–714
Savin A., Sternin B., “Pseudo differential subspaces and their applications in elliptic theory”, C(star)-Algebras and Elliptic Theory, Trends in Mathematics, 2006, 247–289
Savin, A, “Boundary value problems on manifolds with fibered boundary”, Mathematische Nachrichten, 278:11 (2005), 1297
Savin, A, “Elliptic operators on manifolds with singularities and K-homology”, K-Theory, 34:1 (2005), 71
Savin A., Sternin B., “The eta invariant and parity conditions”, Adv. Math., 182:2 (2004), 173–203
Savin A., Schulze B.W., Sternin B., “The eta invariant and elliptic operators in subspaces”, Jean Leray '99 Conference Proceedings - the Karlskrona Conference in Honor of Jean Leray, Mathematical Physics Studies, 24, 2003, 373
A. Yu. Savin, B. Yu. Sternin, “The Eta-Invariant and Pontryagin Duality in K-Theory”, Math. Notes, 71:2 (2002), 245–261
Savin, A, “Elliptic operators in subspaces and the eta invariant”, K-Theory, 27:3 (2002), 253
Savin, AY, “To the problem of homotopy classification of the elliptic boundary value problems”, Doklady Mathematics, 63:2 (2001), 174
Savin A., Schulze B.W., Sternin B., “On the homotopy classification of elliptic boundary value problems”, Partial Differential Equations and Spectral Theory, Operator Theory : Advances and Applications, 126, 2001, 299–305
Anton Savin, Bert-Wolfgang Schulze, Boris Sternin, Partial Differential Equations and Spectral Theory, 2001, 299
Savin, AY, “Subspaces determined by pseudodifferential projection and some applications”, Doklady Akademii Nauk, 371:4 (2000), 448
A. Yu. Savin, B. Yu. Sternin, “Elliptic operators in odd subspaces”, Sb. Math., 191:8 (2000), 1191–1213
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