Introduction to the Theory of Toeplitz Operators with Infinite Index

Inhaltsverzeichnis

• 1 Examples of Toeplitz Operators with Infinite Index Auxiliary material.
• 1.1 The space Lp(?, ?) and the operator S?.
• 1.2 The classes Lp± (?, ?).
• 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 Lp± (?, ?).
• 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.
• 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, ? (?±).
• 3.7 Sine-type functions.
• 3.8 Bases of ent? e functions.
• 3.9 Bases of meromorphic functions.
• 3.10 Boundary interpolation.
• 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 Modelfunction.
• 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.
• 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.
• 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.