Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics

✍ Scribed by Wolfgang Arendt, Ralph Chill, Yuri Tomilov (eds.)

• Publisher: Birkhäuser Basel
• Year: 2015
• Tongue: English
• Leaves: 490
• Series: Operator Theory: Advances and Applications 250
• Edition: 1
• Category: Library

✦ Synopsis

This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrödinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor.

The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. The aim of the conference was to bring together prominent experts in the field of modern semigroup theory, harmonic analysis, complex analysis and mathematical physics, and to present the lively interactions between all of those areas and beyond. In addition, the meeting honored the sixtieth anniversary of Prof C. J. K. Batty, whose scientific achievements are an impressive illustration of the conference goal. These proceedings present contributions by prominent scientists at this international conference, which became a landmark event.

They will be a valuable and inspiring source of information for graduate students and established researchers.

✦ Table of Contents

Front Matter....Pages i-ix
Polynomial Internal and External Stability of Well-posed Linear Systems....Pages 1-16
Countable Spectrum, Transfinite Induction and Stability....Pages 17-29
Maximal Regularity in Interpolation Spaces for Second-order Cauchy Problems....Pages 31-48
Stability of Quantum Dynamical Semigroups....Pages 49-66
Families of Operators Describing Diffusion Through Permeable Membranes....Pages 67-85
Multiscale Unique Continuation Properties of Eigenfunctions....Pages 87-105
Dichotomy Results for Norm Estimates in Operator Semigroups....Pages 107-118
Estimates on Non-uniform Stability for Bounded Semigroups....Pages 119-131
Convergence of the Dirichlet-to-Neumann Operator on Varying Domains....Pages 133-146
A Banach Algebra Approach to the Weak Spectral Mapping Theorem for Locally Compact Abelian Groups....Pages 147-154
Regularity Properties of Sectorial Operators: Counterexamples and Open Problems....Pages 155-170
Global Existence Results for the Navier–Stokes Equations in the Rotational Framework in Fourier–Besov Spaces....Pages 171-197
Some Operator Bounds Employing Complex Interpolation Revisited....Pages 199-211
Generation of Subordinated Holomorphic Semigroups via Yosida’s Theorem....Pages 213-239
A Quantitative Coulhon–Lamberton Theorem....Pages 241-252
An Analytic Family of Contractions Generated by the Volterra Operator....Pages 253-271
Lattice Dilations of Bistochastic Semigroups....Pages 273-279
Domains of Fractional Powers of Matrix-valued Operators: A General Approach....Pages 281-285
General Mazur–Ulam Type Theorems and Some Applications....Pages 287-296
Traces of Non-regular Vector Fields on Lipschitz Domains....Pages 297-309
A Murray–von Neumann Type Classification of C*-algebras....Pages 311-342
Well-posedness viaMonotonicity – an Overview....Pages 343-351
Perturbations of Exponential Dichotomies for Hyperbolic Evolution Equations....Pages 353-368
Gaussian and non-Gaussian Behaviour of Diffusion Processes....Pages 369-395
On Self-adjoint Extensions of Symmetric Operators....Pages 397-452
....Pages 453-461

✦ Subjects

Partial Differential Equations; Operator Theory; Mathematical Applications in the Physical Sciences; Functional Analysis