The Plancherel Theorem for a Reductive Symmetric Space -- The Paley—Wiener Theorem for a Reductive Symmetric Space -- The Plancherel Formula on Reductive Symmetric Spaces from the Point of View of the Schwartz Space.Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three indepen…
Results on topological spaces -- Rings and modules -- Integral extensions -- Factorial rings -- Field extensions -- Finitely generated algebras -- Gradings and filtrations -- Inductive limits -- Sheaves of functions -- Jordan decomposition and some basic results on groups -- Algebraic sets -- Prevarieties and varieties -- Projective varieties -- Dimension -- Morphisms and dimension -- Tangent s…
Introduction -- 1. Preliminaries on Markov-Feller Operators -- 2. The KBBY Decomposition -- 3. Unique Ergodicity -- 4. Equicontinuity -- Bibliography -- Index.In this book invariant probabilities for a large class of discrete-time homogeneous Markov processes known as Feller processes are discussed. These Feller processes appear in the study of iterated function systems with probabilities, conv…
Plane Algebraic Curves -- Ane Algebraic Curves -- Projective Algebraic Curves -- The Coordinate Ring of an Algebraic Curve and the Intersections of Two Curves -- Rational Functions on Algebraic Curves -- Intersection Multiplicity and Intersection Cycle of Two Curves -- Regular and Singular Points of Algebraic Curves. Tangents -- More on Intersection Theory. Applications -- Rational Maps. Parame…
Problems and Tricks -- Number Theory -- Some Applications of Elementary Number Theory -- Ideas and Theories -- Induction and Recursion -- Arithmetic of algebraic numbers -- Arithmetic of algebraic varieties -- Zeta Functions and Modular Forms -- Fermat’s Last Theorem and Families of Modular Forms -- Analogies and Visions -- Introductory survey to part III: motivations and description -- Arake…
Numerical Invariants of a Rees Algebra -- Hilbert Functions and Multiplicities -- Depth and Cohomology of Rees Algebras -- Divisors of a Rees Algebra -- Koszul Homology -- Integral Closure of Algebras -- Integral Closure and Normalization of Ideals -- Integral Closure of Modules -- HowTo.Integral Closure gives an account of theoretical and algorithmic developments on the integral closure of alg…
Parafree Groups -- The Finitary Andrews-Curtis Conjecture -- Cuts in Kähler Groups -- Algebraic Mapping-Class Groups of Orientable Surfaces with Boundaries -- Solved and Unsolved Problems Around One Group -- Cubature Formulas, Geometrical Designs, Reproducing Kernels, and Markov Operators -- Survey on Classifying Spaces for Families of Subgroups -- Are Unitarizable Groups Amenable? -- Probabil…
Kohn's Proof of the Hypoellipticity of the Hörmander Operators -- Compactness Criteria for the Resolvent of Schrödinger Operators -- Global Pseudo-differential Calculus -- Analysis of some Fokker-Planck Operator -- Return to Equillibrium for the Fokker-Planck Operator -- Hypoellipticity and Nilpotent Groups -- Maximal Hypoellipticity for Polynomial of Vector Fields and Spectral Byproducts -- …
The Basic Spaces -- The General Möbius Group -- Length and Distance in ? -- Planar Models of the Hyperbolic Plane -- Convexity, Area, and Trigonometry -- Nonplanar models.The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, suitable for third or …
Part I: Foundations and Computations: Deloopings in Algebraic K- theory -- The Motivic Spectral Sequence -- K-theory of truncated polynomial algebras -- Bott Periodicity in Topological, Algebraic and Hermitian K-theory -- Algebraic K-theory of Rings and Integers in Local and Global Fields. Part II: K-theory and Algebraic Geometry: Motivic Cohomology, K-theory and topological cyclic Homology -- …