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AuthorDybin, Vladimir. author
TitleIntroduction to the Theory of Toeplitz Operators with Infinite Index [electronic resource] / by Vladimir Dybin, Sergei M. Grudsky
ImprintBasel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2002
Connect tohttp://dx.doi.org/10.1007/978-3-0348-8213-2
Descript XII, 300 p. online resource

CONTENT

1 Examples of Toeplitz Operators with Infinite Index Auxiliary material -- 1.1 The space Lp(?, ?) and the operator S? -- 1.2 The classes Lpยฑ (?, ?) -- 1.3 Normally solvable operators -- 1.4 Toeplitz operators -- Examples of operators with infinite index -- 1.5 Blaschke products -- 1.6 An elementary singular function -- 1.7 Boundary degeneracy -- References and comments -- 2 Factorization and Invertibility -- (p, ?)-factorization and (?-theory -- 2.1 The space Lp(?, ?) and the operator S? -- 2.2 Classes of bounded and continuous functions -- 2.3 The classes Lpยฑ (?, ?) -- 2.4 The class fact(p, ?) -- 2.5 A sufficient condition for (p, ?)-factorizability -- Factorization and Toeplitz operators with infinite index -- 2.6 Inner-outer factorization -- 2.7 The class fact(?, p, ?) and one-sided invertibility -- 2.8 Examples of functions in fact(?, p, ?) -- 2.9 The argument of a Blaschke product -- 2.10 The argument of an outer function -- References and comments -- 3 Model Subspaces Model operator and model subspaces -- 3.1 Model subspaces -- 3.2 Deformation of the contour -- 3.3 Model subspaces on ? -- 3.4 Boundary behavior -- Bases and interpolation in model subspaces -- 3.5 Bases -- 3.6 The Carleson condition and interpolation in Hp, ? (?ยฑ) -- 3.7 Sine-type functions -- 3.8 Bases of ent?e functions -- 3.9 Bases of meromorphic functions -- 3.10 Boundary interpolation -- References and comments -- 4 Toeplitz Operators with Oscillating Symbols Almost periodic discontinuities -- 4.1 Uniformly almost periodic functions -- 4.2 Model subspaces on bounded smooth curves -- 4.3 Standard almost periodic discontinuities -- 4.4 Well-posed problems for the Toeplitz equation -- 4.5 General discontinuities of almost periodic type -- Semi-almost periodic discontinuities -- 4.6 The class SAP -- 4.7 Model function -- 4.8 Generalized factorization of SAP functions -- 4.9 Model subspaces -- Wh?l points of power type -- 4.10 Two-sided wh?ls -- 4.11 One-sided wh?ls -- References and comments -- 5 Generalized Factorization of u-periodic Functions and Matrix Functions -- 5.1 Block Toeplitz operators -- 5.2 Generalized factorization of matrix functions -- 5.3 u-periodic matrix functions -- 5.4 Infinite index of logarithmic type -- 5.5 Infinite index of arbitrary order -- 5.6 Sufficient conditions for the theorem on -- general oscillations. Examples -- 5.7 Slow oscillations -- 5.8 Modelling of oscillations -- 5.9 Generalized almost periodic discontinuities -- 5.10 Generalized matrix periodic discontinuities -- References and comments -- 6 Toeplitz Operators Whose Symbols Have Zeros -- The normalization principle -- 6.1 Normally solvable operators -- 6.2 Normalization of linear operators -- Normalization of Toeplitz operators -- 6.3 Symbols with polynomial degeneracy -- 6.4 Symbols with locally-polynomial degeneracy -- 6.5 Basic examples -- References and comments -- References


Mathematics Mathematical analysis Analysis (Mathematics) Mathematics Analysis



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