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.

El Mustapha Ait Benhassi, Said Boulite, Lahcen Maniar, Roland Schnaubelt: Polynomial internal and external stability of well-posed linear systems.- R. J. Archbold, D. W. B. Somerset: Minimal primal ideals in the multiplier algebra of a C0(X)-algebra.- Wolfgang Arendt: Countable spectrum, transfinite induction, and stability.- Charles Batty, Ralph Chill, Sachi Srivastava: Maximal regularity in interpolation spaces for second order Cauchy problems.- B. V. Rajarama Bhat, Sachi Srivastava: Stability of quantum dynamical semigroups.- Adam Bobrowski: Families of operators describing diffusion through permeable membranes.- Denis Borisov, Ivica Nakic, Christian Rose, Martin Tautenhahn, Ivan Veselic: Multiscale unique continuation properties of eigenfunctions.- Isabelle Chalendar, Jean Esterle, Jonathan Partington: Dichotomy results for norm estimates in operator semigroups.- Thomas Duyckaerts: Estimates on non-uniform stability for bounded semigroups.- A. F. M. ter Elst, El Maati Ouhabaz: Convergence of the Dirichlet-to-Neumann operator on varying domains.- Jean Esterle, Eva Fasangová: A Banach algebra approach to the weak spectral mapping theorem for locally compact abelian groups.- Stephan Fackler: Regularity properties of sectorial operators: counterexamples and open problems.- Daoyuang Fang, Bin Han, Matthias Hieber: Global existence results for the Navier-Stokes equations in the rotational framework.- Fritz Gesztesy, Yuri Latushkin, Fedor Sukochev, Yuri Tomilov: Some operator bounds employing complex interpolation revisited.- Alastair Gillespie: Power bounded invertible operators and invertible isometries on L^p spaces.- Alexander Gomilko, Yuri Tomilov: Generation of subordinated holomorphic semigroups via Yosida's theorem.- Tuomas Hytönen: A quantitative Coulhon-Lamberton theorem.- L. Khadkuu, D. Tsedenbayar, Jaroslav Zemanek: An analytic family of contractions generated by the Volterra operator.- Leonhard J. Konrad: Lattice dilations for bistochastic semigroups.- Irena Lasiecka, Roberto Triggiani: Domains of fractional powers of matrix-valued operators: a general approach.- Lajos Molnar: General Mazur-Ulam type theorems and some applications.- Sylvie Monniaux: Traces of non regular vector fields on Lipschitz domains.- Jan van Neerven: The L^p-Poincaré inequality for analytic Ornstein-Uhlenbeck operators.- Chi-Keung Ng, Ngai-Ching Wong: A Murray-von Neumann type classification of C*-algebras.- Rainer Picard, Sascha Trostor, Marcus Waurick: Wellposedness via monotonicity.- Jan Prüß: Perturbations of exponential dichotomies for hyperbolic evolution equations.- Derek Robinson: Gaussian and non Gaussian behaviour of diffusion processes.- Felix Schwenninger, Hans Zwart: Functional calculus for C0-semigroups using infinite-dimensional systems theory.- Jürgen Voigt: On self-adjoint extensions of symmetric operators.