Around the Research of Vladimir Maz'ya III: Analysis and Applications

ISBN-13: 9781461425519 / Angielski / Miękka / 2012 / 386 str.

Ari Laptev

Opis

The topics of this volume are diverse, but all of them are related to a huge area in analysis and applications where remarkably deep results and original approaches of Professor Maz'ya play a fundamental role. World-recognized experts present their new results covering, in particular, the following topics: Beurling's minimum principle, inverse hyperbolic problems, degenerate oblique derivative problems, the Lp-dissipativity connected with the Lp-contractivity of the generated semigroups, optimal control of a biharmonic obstacle problem sharp bilateral bounds of Green's function for the fractional Schrodinger operator, Bergman orthogonal polynomials, some class of singular integral operators, general Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities, the Laplace operator on domains with rough boundaries, integral and supremum operators, finite rank Toeplitz operators in the Bergman space, bounds on the resolvent of a non-selfadjoint pseudodifferential operator, the Faber-Krahn inequality, and some other topics.

Spis treści

Optimal Control of a Biharmonic Obstacle Problem, D. Adams et al.- Minimal Thinness and Beurling's Minimum Principle, H. Aikawa.- Progress in the Problem of Lp-Contractivity of Semigroups for Partial Differential Operators, A. Cialdea.- Uniqueness and Nonuniqueness in Inverse Hyperbolic Problems and the Black Hole Phenomenon, G. Eskin.- Global Green's Function Estimates, M.W. Frazier, I.E. Verbitsky.- On Spectral Minimal Partitions: the Case of the Sphere, B. Helffer et al.- Weighted Sobolev Space Estimates for a Class of Singular Integral Operators, D. Mitrea et al.- On general Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities, S. Molchanov, B. Vainberg.- Estimates for the Counting Function of the Laplace Operator on Domains with Rough Boundaries, Y. Netrusov, Y. Safarov.- W2,p-Theory of the Poincaré Problem, D.K. Palagachev.- Weighted Inequalities for Integral and Supremum Operators, L. Pick.- Finite Rank Toeplitz Operators in the Bergman Space, G. Rozenblum.- Resolvent Estimates for Non-Selfadjoint Operators via Semigroups, J. Sjöstrand.

Blurb

International Mathematical Series Volume 13
Around the Research of Vladimir Ma'z'ya III
Analysis and Applications
Edited by Ari Laptev

More than 450 research articles and 20 books by Prof. Maz'ya contain numerous fundamental results and fruitful techniques which have strongly influenced the development of many branches in Analysis and, in particular, the topics discussed in this volume: problems with biharmonic differential operators, the minimal thinness of nontangentially accessible domains, the Lp-dissipativity of partial differential operators and the Lp-contractivity of the generated semigroups, uniqueness and nonuniqueness in inverse hyperbolic problems and the existence of black (white) holes, global exponential bounds for Green's functions for differential and integral equations with possibly singular coefficients, data, and boundaries of the domains, properties of spectral minimal partitions, the boundedness of integral operators from Besov spaces on the boundary of a Lipschitz domain into weighted Sobolev spaces of functions in the domain, the Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities for operators on functions in metric spaces, spectral problems with the Schrodinger operator, the Weyl formula for the Laplace operator on a domain under minimal assumptions on the boundary, a degenerate oblique derivative problem for second order uniformly elliptic operators, weighted inequalities with the Hardy operator in the integral and supremum form, finite rank Toeplitz operators and applications, the resolvent of a non-selfadjoint pseudodifferential operator.

Contributors include: David R. Adams (USA), Volodymyr Hrynkiv (USA), and Suzanne Lenhart (USA); Hiroaki Aikawa (Japan); Alberto Cialdea (Italy); Gregory Eskin (USA); Michael W. Frazier (USa) and Igor E. Verbitsky (USA); Bernard Helffer (France), Thomas Hoffmann-Ostenhof (Austria), and Susanna Terracini (italy); Dorina Mitrea (USA), Marius Mitrea (USA), and Sylvie Monniaux (France); Stanislav Molchanov (USA) and Boris Vainberg (USA); Yuri Netrusov (UK) and Yuri Safarov (UK); Dian K. Palagachev (Italy); Lubos Pick (Czech Republic); Grigori Rozenblum (Sweden); Johannes Sjostrand (France).

Ari Laptev
Imperial College London (UK) and
Royal Institute of Technology (Sweden)
Ari Laptev is a world-recognized specialist in Spectral Theory of
Differential Operators. He is the President of the European Mathematical
Society for the period 2007- 2010.

Tamara Rozhkovskaya
Sobolev Institute of Mathematics SB RAS (Russia)
and an independent publisher
Editors and Authors are exclusively invited to contribute to volumes highlighting
recent advances in various fields of mathematics by the Series Editor and a founder
of the IMS Tamara Rozhkovskaya.

Cover image: Vladimir Maz'ya