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

:	Vladimir Rabinovich, S. M. Grudsky, Israel Gohberg, Roland V. Duduchava
:	Roland V. Duduchava, Israel Gohberg, Sergei M. Grudsky, Vladimir Rabinovitch
:	Recent Trends in Toeplitz and Pseudodifferential Operators The Nikolai Vasilevskii Anniversary Volume
:	Birkhäuser Basel
:	9783034605489
:	1
:	CHF 85.30
:

:	Analysis
:	English

:	272
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

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.

	Table of Contents	6
	The Life and Work of Nikolai Vasilevski	9
	On the Structure of the Eigenvectors of Large Hermitian Toeplitz Band Matrices	23
	1. Introduction and main results	23
	2. The first column of the adjugate matrix	29
	3. The main terms of the first column	32
	4. The asymptotics of the eigenvectors	37
	5. Symmetric matrices	39
	6. Numerical results	42
	References	43
	Complete Quasi-wandering Sets and Kernels of Functional Operators	45
	1. Introduction	45
	2. The kernel space of the operator Ua	47
	References	50
	Lions’ Lemma, Korn’s Inequalities and the Lam´e Operator on Hypersurfaces	51
	Introduction	51
	1. Sobolev spaces and Bessel potential operators	56
	2. Lions’ Lemma and Korn’s inequalities	59
	3. Killing’s vector fields and the unique continuation from the boundary	63
	4. A local fundamental solution to the Lame equation	70
	5. BVPs for the Lame equation and Green’s formulae	73
	6. The Dirichlet BVP for the Lame equation	76
	7. The Neumann BVP for the Lame equation	78
	References	82
	On the Bergman Theory for Solenoidal and Irrotational Vector Fields, I: General Theory	86
	1. Introduction	86
	1.1.	86
	1.2.	87
	1.3.	87
	2. Solenoidal and irrotational vector fields: main results	88
	2.1.	88
	2.2. The SI-Bergman space and the SI-Bergman kernel	88
	2.3. SI-Bergman projection	90
	2.4. Decomposition of ˆ L2	90
	2.5. M¨obius transformations in R3 in vectorial language	91
	2.6. R-linear spaces of vector fields and M¨obius transformations on R3	92
	3. The Bergman theory for Moisil-Theodoresco hyperholomorphy	95
	3.1. Preliminaries	95
	3.2. Mobius transformations in R3 in quaternionic terms	96