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The aim of the book is to present new results in operator theory and its applications. In particular, the book is devoted to operators with automorphic symbols, applications of the methods of modern operator theory and differential geometry to some problems of theory of elasticity, quantum mechanics, hyperbolic systems of partial differential equations with multiple characteristics, Laplace-Beltrami operators on manifolds with singular points. Moreover, the book comprises new results in the theory of Wiener-Hopf operators with oscillating symbols, large hermitian Toeplitz band matrices, commutative algebras of Toeplitz operators, and discusses a number of other topics.

Recent Trends in Toeplitz and Pseudodifferential Operators: The Nikolai Vasilevskii Anniversary Volume

Preface.- The life and work of Nikolai Vasilevski.- On the structure of the eigenvectors of large Hermitian Toeplitz band matrices.- Complete quasi-wandering sets and kernels of functional operators.- Lions' lemma, Korn's inequalities and the Lamé operator on hypersurfaces.- On the Bergman theory for solenoidal and irrotational vector fields, I: General theory.- Weighted estimates of generalized potentials in variable exponent Lebesgue spaces on homogeneous spaces.- Wiener-Hopf operators with oscillating symbols on weighted Lebesgue spaces.- On the Ill-posed hyperbolic systems with a multiplicity change point of not less than the third order.- On C*-algebras of super Toeplitz operators with radial symbols.- Universality of some C*-algebra generated by a unitary and a self-adjoint idempotent.- Commutative algebras of Toeplitz operators and Lagrangian foliations.- Exponential estimates of eigenfunctions of matrix Schrödinger and Dirac operators.- The Laplace-Beltrami operator on a rotationally symmetric surface.- On the structure of operators with automorphic symbols.- Hilbert bundles and flat connexions over Hermitian symmetric domains.