Author | Hagen, Roland. author |
---|---|
Title | Spectral Theory of Approximation Methods for Convolution Equations [electronic resource] / by Roland Hagen, Steffen Roch, Bernd Silbermann |
Imprint | Basel : Birkhรคuser Basel, 1995 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-9067-0 |
Descript | 376 p. online resource |
1 Invertibility in Banach algebras -- 1.1 Banach algebras and C*-algebras -- 1.2 Linear operators -- 1.3 Stability of operator sequences -- 1.4 Local principles -- 1.5 The finite section method for Toeplitz operators -- 1.6 A general invertibility scheme -- 1.7 Norm-preserving localization -- 1.8 Exercises -- 1.9 Comments and references -- 2 Spline spaces and Toeplitz operators -- 2.1 Singular integral operators-constant coefficients -- 2.2 Piecewise constant splines -- 2.3 Algebras of Toeplitz operators (Basic facts) -- 2.4 Discretized Mellin convolutions -- 2.5 Algebras of Toeplitz operators (Fredholmness) -- 2.6 General spline spaces -- 2.7 Spline projections -- 2.8 Canonical prebases -- 2.9 Concrete spline spaces -- 2.10 Concrete spline projections -- 2.11 Approximation of singular integral operators -- 2.12 Proofs -- 2.13 Exercises -- 2.14 Comments and references -- 3 Algebras of approximation sequences -- 3.1 Algebras of singular integral operators -- 3.2 Approximation using piecewise constant splines -- 3.3 Approximation of homogeneous operators -- 3.4 The stability theorem -- 3.5 Basic properties of approximation sequences -- 3.6 Proof of the stability theorem -- 3.7 Sequences of local type -- 3.8 Concrete approximation methods -- 3.9 Exercises -- 3.10 Comments and references -- 4 Singularities -- 4.1 Approximation of operators in Toeplitz algebras -- 4.2 Multiindiced approximation methods -- 4.3 Approximation of singular integral operators -- 4.4 Approximation of compound Mellin operators -- 4.5 Approximation over unbounded domains -- 4.6 Exercises -- 4.7 Comments and references -- 5 Manifolds -- 5.1 Algebras of singular integral operators -- 5.2 Splines over homogeneous curves -- 5.3 Splines over composed curves -- 5.4 The stability theorem -- 5.5 A Galerkin method -- 5.6 Exercises -- 5.7 Comments and references -- 6 Finite sections -- 6.1 Finite sections of singular integrals -- 6.2 Finite sections of discrete convolutions -- 6.3 Around spline approximation methods