Dedicated to Tosio Katös 100th birthday, this book contains research and survey papers on a broad spectrum of methods, theories, and problems in mathematics and mathematical physics. Survey papers and in-depth technical papers emphasize linear and nonlinear analysis, operator theory, partial differential equations, and functional analysis including nonlinear evolution equations, the Korteweg¿de Vries equation, the Navier¿Stokes equation, and perturbation theory of linear operators. The Kato inequality, the Kato type matrix limit theorem, the Howland¿Kato commutator problem, the Kato-class of potentials, and the Trotter¿Kato product formulae are discussed and analyzed. Graduate students, research mathematicians, and applied scientists will find that this book provides comprehensive insight into the significance of Tosio Katös impact to research in analysis and operator theory.

Complementarity and Stochastic Independence (Luigi Accardi and Yun-Gang Lu).- Norm Conditions for Separability in Mm ¿Mn (Tsuyoshi Ando).- Kato's Inequality (W. Arendt and A.F.M. ter Elst).- Tosio Kato's Unpublished Paper (Claude Bardos and Hisashi Okamoto).- On the Border Lines Between the Regions of Distinct Solution Type for Solutions of the Friedmann Equation (Hellmut Baumgartel). - Scattering on Leaky Wires in Dimension Three (Pavel Exner and Sylwia Kondej).- Computing Traces, Determinants, and ¿-Functions for Sturm-Liouville Operators: A Survey (Fritz Gesztesy and Klaus Kirsten).- On the Domain of a Magnetic Schrodinger Operator with Complex Electric Potential (Bernard Helffer and Jean Nourrigat).- Matrix Limit Theorems of Kato Type Related to Positive Linear Maps and Operator Means (Fumio Hiai).- The Howland - Kato Commutator Problem (Ira Herbst and Thomas L. Kriete).- Point-wise Exponential Decay of Bound States of the Nelson Model with Kato-class Potentials (Fumio Hiroshima).- Regular KMS States of Weakly Coupled Anharmonic Crystals and the Resolvent CCR Algebra (Tomohiro Kanda and Taku Matsui).- Trotter Product Formula and Linear Evolution Equations on Hilbert Spaces (Hagen Neidhardt, Artur Stephan and Valentin A. Zagrebnov).- Exact solutions to problems with perturbed differential and boundary operators (Ioannis N. Parasidis and Eftymios Providas).- On a Few Equivalent Statements of a Hilbert-Type Integral Inequality in the Whole Plane with the Hurwitz Zeta Function (Themistocles M. Rassias and Bicheng Yang).- Tosio Kato's Work on Non-Relativistic Quantum Mechanics: A Brief Report (Barry Simon).- The Factor Type of Conservative KMS Weights on Graph C*-Algebras (Klaus Thomsen).- Trotter-Kato Product Formulae in Dixmier Ideal (Valentin A. Zagrebnov).