## Recent Trends in Operator Theory and Partial Differential Equations: The Roland Duduchava Anniversary VolumeVladimir Maz'ya, David Natroshvili, Eugene Shargorodsky, Wolfgang L. Wendland This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory, approximation theory, and reflects the broad spectrum of Roland Duduchava's research. The book is addressed to a wide audience of pure and applied mathematicians. |

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### Contents

The DuduchavaRoch Formula | 1 |

Convolution Type Operators with Symmetry in Bessel Potential Spaces | 21 |

On Symmetries of the FeinbergZee Random Hopping Matrix | 50 |

Inequalities of BabuškaAziz and FriedrichsVelte for Differential Forms | 79 |

High Frequency Oscillations of First Eigenmodes in Axisymmetric Shells as the Thickness Tends to Zero | 89 |

Kernels of WienerHopf plus Hankel Operators with Matching Generating Functions | 111 |

Spline Galerkin Methods for the Double Layer Potential Equations on Contours with Corners | 129 |

Calgebras of Bergman Type Operators with Piecewise Continuous Coefficients over Bounded Polygonal Domains | 145 |

Solvability and Lyapunov Stability of a Twocomponent System of Generalized PoissonNernstPlanck Equations | 172 |

A Local Uniqueness Result for a Quasilinear Heat Transmission Problem in a Periodic Twophase Dilute Composite | 193 |

The Method of Potential Operators for Anisotropic Helmholtz Operators on Domains with Smooth Unbounded Boundaries | 228 |

Gabor Analysis for Schrödinger Equations and Propagation of Singularities | 257 |

Commutative Algebras of Toeplitz Operators on a Siegel Domain Associated with the Nilpotent Group of Its Biholomorphisms | 275 |

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Advances and Applications algebra Anal analytic Appl asymptotics Banach Bergman Bergman space Birkhäuser boundary value problems bounded C*-algebra coefficients computed consider convergence convolution Corollary curves defined denote Differential Equations Dirichlet domain Duduchava eigenvalue elliptic eoſ equivalent factorization filled Julia set finite formula Fredholm Fredholm operator functions Galerkin method given Hankel operators Hº ÖD implies inequality infinity integral equations invertible isomorphism kernels Laplace operator Lemma limit operators linear Lipschitz domains Math Mathematical matrix Natroshvili nonlinear normal numbers obtain Op(a Operator Theory ºrn piecewise polynomial Proof properties Proposition pseudodifferential operators satisfies Section sequence shells singular integral operators solution space spline Galerkin method subsets subspace symbols Theorem Toeplitz operators vector Wiener–Hopf Σπ