## Topics in Operator Theory: Volume 2: Systems and Mathematical PhysicsJoseph A. Ball, Vladimir Bolotnikov, J. William Helton, Leiba Rodman, Ilya M. Spitkovsky This is a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications. The intended audience are mathematicians, physicists, electrical engineers in academia and industry, researchers and graduate students, that use methods of operator theory and related fields of mathematics, such as matrix theory, functional analysis, differential and difference equations, in their work. |

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### Contents

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Absence of Existence and Uniqueness for Forwardbackward Parabolic Equations on a Halfline | 89 |

Bounds for Eigenvalues of the pLaplacian with Weight Function of Bounded Variation | 99 |

The GelfandLevitan Theory for Strings | 114 |

On the Uniqueness of a Solution to Anisotropic Maxwells Equations | 137 |

Dichotomy and Boundedness of Solutions for Some Discrete Cauchy Problems | 165 |

Control Laws for Discrete Linear Repetitive Processes with Smoothed Previous Pass Dynamics | 175 |

Additive Invariants on Quantum Channels and Regularized Minimum Entropy | 237 |

A Functional Model Eigenvalues and Finite Singular Critical Points for Indefinite SturmLiouville Operators | 246 |

On the Eigenvalues of the Lax Operator for the Matrixvalued AKNS System | 289 |

An Extension Theorem for Bounded Forms Defined in Relaxed Discrete Algebraic Scattering Systems and the Relaxed Commutant Lifting Theorem | 324 |

Dirac and SemiDirac Pairs | 347 |

Mapping Properties of Layer Potentials Associated with Higherorder Elliptic Operators in Lipschitz Domains | 363 |

Applications of a Numerical Spectral Expansion Method to Problems in Physics a Retrospective | 408 |

Regularized Perturbation Determinants and KdV Conservation Laws for Irregular Initial Profiles | 427 |

Fourier Method for Onedimensional Schrodinger Operators with Singular Periodic Potentials | 195 |

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algebraic scattering system Applications assume assumption asymptotic Birkhäuser boundary conditions bounded Lipschitz domain coefficients Commutant Lifting Commutant Lifting Theorem consider constant coprime corresponding curl defined denote differential equations differential operators Dirac operators Dirichlet discrete double coprime factorization eigenvalues equivalent exists finite formula Fourier frequency-domain given gº e G H∞-problem Hence Hilbert space holds implies integral equation interpolation inverse kernel Krein space layer potential Lemma Lipschitz domain mapping Math Mathematics Mathematics Subject Classification matrix method modally multiplicity noncommutative norm notation Note obtain Operator Theory pair parameter polydisk polynomial problem proof properties Proposition quantum channel realization representation result satisfy Section self-adjoint self-adjoint operator sesquilinear form singular ſº spectral function spectral theory spectrum stabilizable stabilizing controllers state-space Sturm-Liouville operators subspace symmetric triplet vector