Series: Operator Theory: Advances and Applications, Vol. 226
Subseries: Linear Operators and Linear Systems
2012,Approx. 320 p.
Hardcover
ISBN 978-3-0348-0427-1
Due: July 31, 2012
The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parameter sequences. Schur analysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricial generalizations. These problems include interpolation and moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices.
This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrix-valued Caratheodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.?
Content Level ≫ Research
Keywords ≫ Caratheodory and Nevanlinna classes - Schur analysis - Schur-type algorithms - matrix versions of power moment problems
Related subjects ≫ Analysis
Series: Lecture Notes in Mathematics, Vol. 2050
2012, Approx. 450 p. 2 illus., 1 in color.
Softcover
ISBN 978-3-642-29848-6
Due: July 31, 2012
This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) from the years 2006 to 2011 continues the long tradition of the previous volumes, which reflect the general trends of Asymptotic Geometric Analysis, understood in a broad sense, and are a source of inspiration for new research.
Most of the papers deal with various aspects of the theory, including classical topics in the geometry of convex bodies, inequalities involving volumes of such bodies or more generally, logarithmically-concave measures, valuation theory, probabilistic and isoperimetric problems in the combinatorial setting, volume distribution on high-dimensional spaces and characterization of classical constructions in Geometry and Analysis (like the Legendre and Fourier transforms, derivation and others). All papers here are original research papers.
The α-Cosine Transform and Intertwining Integrals on Real Grassmannians.- On Modules Over Valuations.- On Multiplicative Maps of Continuous and Smooth Functions.- Order Isomorphisms on Convex Functions in Windows.- Finite Transitive Graph Embeddings into a Hyperbolic.- Metric Space Must Stretch or Squeeze.- Tightness of Fluctuations of First Passage Percolation on Some Large Graphs.- Finitely Supported Measures on SL2(R) which are Absolutely Continuous at Infinity.- Interpolations, Convexity and Geometric Inequalities.- Hypercontractive Measures, Talagrand's Inequality, and Inuences.- A Family of Unitary Operators Satisfying a Poisson-Type Summation Formula.- Stability of Order Preserving Transforms.- On the Distribution of the 2-Norm of Linear Functionals on Isotropic Convex Bodies.- A Remark on Vertex Index of the Convex Bodies.- Inner Regularization of Log-Concave Measures and Small-Ball Estimates.- An Operator Equation Generalizing the Leibniz Rule for the Second Derivative.- Moments of Unconditional Logarithmically Concave Vectors.- Projections of Probability Distributions: A Measure-Theoretic Dvoretzky Theorem.- On a Loomis-Whitney Type Inequality for Permutationally Invariant Unconditional Convex Bodies.- The Hormander Proof of the Bourgain-Milman Theorem.- On Some Extension of Feige's Inequality.- On the Mean Width of Log-Concave.- Approximate Gaussian Isoperimetry for k Sets.- Remark on Stability of Brunn-Minkowski and Isoperimetric Inequalities for Convex Bodies.- On Contact Points of Convex Bodies
Series: Lecture Notes in Mathematics, Vol. 2051
Subseries: C.I.M.E. Foundation Subseries
2012, 2012, X, 190 p. 12 illus., 1 in color.
Softcover
ISBN 978-3-642-29510-2
Due: July 31, 2012
The book is based on the lectures given at the CIME school "Quantum many body systems" held in the summer of 2010. It provides a tutorial introduction to recent advances in the mathematics of interacting systems, written by four leading experts in the field: V. Rivasseau illustrates the applications of constructive Quantum Field Theory to 2D interacting electrons and their relation to quantum gravity; R. Seiringer describes a proof of Bose-Einstein condensation in the Gross-Pitaevski limit and explains the effects of rotating traps and the emergence of lattices of quantized vortices; J.-P. Solovej gives an introduction to the theory of quantum Coulomb systems and to the functional analytic methods used to prove their thermodynamic stability; finally, T. Spencer explains the supersymmetric approach to Anderson localization and its relation to the theory of random matrices. All the lectures are characterized by their mathematical rigor combined with physical insights.
Introduction to the Renormalization Group with Applications to Non-Relativistic Quantum Electron Gases.- Cold Quantum Gases and Bose-Einstein Condensation.- Quantum Coulomb gases.- SUSY Statistical Mechanics and Random Band Matrices.
Series: Lecture Notes in Mathematics, Vol. 2052
2012, 2012, X, 300 p.
Softcover Information
ISBN 978-3-642-29513-3
Due: July 31, 2012
This text deals with A<sup>1</sup>-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A<sup>1</sup>-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to the properties and computations of A<sup>1</sup>-homotopy sheaves, A<sup>1</sup>-homotogy sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties.
1 Introduction.- 2 Unramified sheaves and strongly A1-invariant sheaves.- 3 Unramified Milnor-Witt K-theories.- 4 Geometric versus canonical transfers.- 5 The Rost-Schmid complex of a strongly A1-invariant sheaf.- 6 A1-homotopy sheaves and A1-homology sheaves.- 7 A1-coverings.- 8 A1-homotopy and algebraic vector bundles.- 9 The affine B.G. property for the linear groups and the Grassmanian