Recent trends in Toeplitz and pseudodifferential operators. [and others], Editors the Nikolai Vasilevskii anniversary volume

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. Title Page ......Page 3 Copyright Page ......Page 4 Table of Contents ......Page 5 The Life and Work of Nikolai Vasilevski......Page 8 1. Introduction and main results......Page 22 2. The first column of the adjugate matrix......Page 28 3. The main terms of the first column......Page 31 4. The asymptotics of the eigenvectors......Page 36 5. Symmetric matrices......Page 38 6. Numerical results......Page 41 References......Page 42 1. Introduction......Page 44 2. The kernel space of the operator Uα......Page 46 References......Page 49 Introduction......Page 50 1. Sobolev spaces and Bessel potential operators......Page 55 2. Lions’ Lemma and Korn’s inequalities......Page 58 3. Killing’s vector fields and the unique continuation from the boundary......Page 62 4. A local fundamental solution to the Lame equation......Page 69 5. BVPs for the Lame equation and Green’s formulae......Page 72 6. The Dirichlet BVP for the Lame equation......Page 75 7. The Neumann BVP for the Lame equation......Page 77 References......Page 81 1.1.......Page 85 1.3.......Page 86 2.2. The SI-Bergman space and the SI-Bergman kernel......Page 87 2.4. Decomposition of ˆ L2......Page 89 2.5. M ̈obius transformations in R3 in vectorial language......Page 90 2.6. R-linear spaces of vector fields and M ̈obius transformations on R3......Page 91 3.1. Preliminaries......Page 94 3.2. Mobius transformations in R3 in quaternionic terms......Page 95 3.3. Mobius transformations and hyperholomorphy......Page 96 3.4. Some properties of quaternionic Hilbert spaces......Page 98 3.5. The hyperholomorphic Bergman space......Page 99 3.6. Mobius transformations in R3 and function spaces......Page 103 3.7. Decomposition of the space L2꤀Ⰰ䠀......Page 105 4.1. Preliminaries......Page 106 4.2. Proofs of the statements of Section 2......Page 108 References......Page 111 1. Introduction......Page 113 2. Formulation of the main result......Page 115 3. Auxiliary estimates......Page 117 4. Main lemma......Page 120 5. Proof of the main result......Page 124 References......Page 126 1. Introduction......Page 129 2.1. Slowly oscillating Fourier multipliers on Lp刀Ⰰ眀......Page 132 2.2. Limit operators and the fiber M∞嬀匀伀Ⰰ 匀䄀倀崀......Page 133 2.3. Wiener-Hopf operators with almost periodic symbols......Page 135 3. Geometric mean for matrix functions in [APp]N×N......Page 136 4. Necessary Fredholm conditions......Page 139 5. Regularizers of Wiener-Hopf operators with symbols in SAPp,w......Page 141 6. Wiener-Hopf operators with symbols in [SOp,w, SAPp,w]......Page 142 7. Matrix case......Page 148 References......Page 150 1. Main results......Page 152 2. Ramifications of trajectories......Page 158 3. Proof of the theorem......Page 164 4. Addition......Page 175 References......Page 178 1. Introduction......Page 180 2. Super Toeplitz operators on the unit disk......Page 181 3. Action of the super circle on the super disk......Page 184 4. Radial functions: S1|1-invariant functions......Page 186 5. Super Toeplitz operators with radial symbols......Page 188 References......Page 192 1. Introduction......Page 194 2. The main result and its proof......Page 195 References......Page 198 1. Introduction......Page 199 2. Preliminaries on symplectic geometry and foliations......Page 201 3. Berezin’s correspondence principle for bounded domains......Page 202 4. Proofs of the main results......Page 203 References......Page 204 1. Introduction......Page 206 2.1. Essential spectrum......Page 207 2.2. Exponential estimates......Page 209 3.1. Essential spectrum......Page 210 3.2. Exponential estimates of eigenfunctions of the discrete spectrum......Page 212 4.1. Essential spectrum of Dirac operators......Page 214 4.2. Exponential estimates of eigenfunctions of the Dirac operator......Page 216 References......Page 217 Introduction......Page 220 1. Geometry......Page 222 2. Laplace-Beltrami operator......Page 223 3. Weighted spaces......Page 224 4. Resolvent......Page 227 5. Fredholm theory......Page 229 6. Asymptotics......Page 230 7. Index formula......Page 232 References......Page 233 1. Introduction......Page 235 2. Operators with automorphic symbols......Page 236 3. Some automorphic operators......Page 238 4. The distribution T∞......Page 241 5. Other symbolic calculi......Page 242 References......Page 250 0. Introduction......Page 251 1. The canonical connexion on a Hilbert subbundle......Page 252 2. The Fock bundle of entire functions......Page 256 3. Fock bundles for Jordan algebra representations......Page 263 4. The Jordan theoretic framework......Page 268 References......Page 273