## The Extended Field of Operator TheoryAs this volume demonstrates, at roughly 100 years of age operator theory remains a vibrant and exciting subject area with wide ranging applications. Many of the th papers found here expandon lectures givenat the 15 International Workshop on Operator Theory and Its Applications, held at the University of Newcastle upon th th Tyne from the 12 to the 16 of July 2004. The workshop was attended by close to 150 mathematicians from throughout the world, and is the ?rst IWOTA to be held in the UK. Talks ranged over such subjects as operator spaces and their - plications, invariant subspaces, Kre? ?n space operator theory and its applications, multivariate operator theory and operator model theory, applications of operator theory to function theory, systems theory including inverse scattering, structured matrices, and spectral theory of non-selfadjoint operators, including pseudodi?- ential and singular integral operators. These interests are re?ected in this volume. As with all of the IWOTA proceedings published by Birkh ̈ auser Verlag, the - pers presented here have been refereed to the same high standards as those of the journal Integral Equations and Operator Theory. BANACH C* ALGEBRAS H CONTROL HILBERT KREIN OPERATOR THEORY INTERPOLATION VON NEUMANN A few words about the above image which graced the workshop programme and bag. In commuting between home in Hexham and work in Newcastle, I often x Editorial Preface travel by train. |

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### Contents

Inverse Scattering to Determine the Shape of a Vocal Tract | 1 |

Positivity and the Existence of Unitary Dilations of Commuting Contractions | 17 |

The Infinitedimensional Continuous Time KalmanYakubovichPopov Inequality | 36 |

From Toeplitz Eigenvalues through Greens Kernels to Higherorder WirtingerSobolev Inequalities | 73 |

The Method of Minimal Vectors Applied to Weighted Composition Operators | 89 |

The Continuous Analogue of the Resultant and Related Convolution Operators | 106 |

Split Algorithms for Centrosymmetric ToeplitzplusHankel Matrices with Arbitrary Rank Profile | 129 |

SchmidtRepresentation of Difference Quotient Operators | 147 |

Pseudodifferential Operators with Compound Slowly Oscillating Symbols | 189 |

Extension of Operator Lipschitz and Commutator Bounded Functions | 225 |

On the Kernel of Some Onedimensional Singular Integral Operators with Shift | 245 |

The Fredholm Property of Pseudodifferential Operators with Nonsmooth Symbols on Modulation Spaces | 258 |

On Indefinite Cases of Operator Identities Which Arise in Interpolation Theory | 281 |

Singular Integral Operators in Weighted Spaces of Continuous Functions with Oscillating Continuity Moduli and Oscillating Weights | 323 |

PolyBergman Spaces and Twodimensional Singular Integral Operators | 349 |

Weak Mixing Properties of Vector Sequences | 360 |

Algebras of Singular Integral Operators with Piecewise Continuous Coefficients on Weighted Nakano Spaces | 171 |

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Advances and Applications algorithms Banach algebra Banach space belongs Birkhäuser Verlag bounded linear operator boundedness Cayley transform centrosymmetric coefficients commutator compact continuous function converges Corollary curve defined Definition denote eigenvalue equivalent exists finite follows formula Fredholm Fredholm theory given Gohberg H-passive Hence Hilbert space Hölder spaces implies Integral Equations inverse Jordan chain Karlovich kernel KYP inequality Lebesgue spaces Lemma limit operators Math matrix functions minimal mixing to zero Nakano spaces norm obtain Operator Theory orthogonal polynomial problem Proof of Theorem Proposition prove pseudo-similarity operator pseudodifferential operators QeZ2N representation result Samko satisfies Section selfadjoint semigroup singular integral operators slowly oscillating solution spectral subset subspaces symbols symmetric system node Theorem 4.5 Toeplitz transfer function uniformly unitary dilation vector vocal tract weak mixing weakly mixing weighted

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