TY - INPR A1 - Savin, Anton A1 - Sternin, Boris T1 - Pseudodifferential subspaces and their applications in elliptic theory N2 - The aim of this paper is to explain the notion of subspace defined by means of pseudodifferential projection and give its applications in elliptic theory. Such subspaces are indispensable in the theory of well-posed boundary value problems for an arbitrary elliptic operator, including the Dirac operator, which has no classical boundary value problems. Pseudodifferential subspaces can be used to compute the fractional part of the spectral Atiyah–Patodi–Singer eta invariant, when it defines a homotopy invariant (Gilkey’s problem). Finally, we explain how pseudodifferential subspaces can be used to give an analytic realization of the topological K-group with finite coefficients in terms of elliptic operators. It turns out that all three applications are based on a theory of elliptic operators on closed manifolds acting in subspaces. T3 - Preprint - (2005) 17 KW - elliptic operator KW - boundary value problem KW - pseudodifferential subspace KW - dimension functional KW - η-invariant KW - index KW - modn-index KW - parity condition Y1 - 2009 UR - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/2825 UR - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-29937 ER -