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Dynamics of Linear Operators
The first book to assemble the wide body of theory which has rapidly developed on the dynamics of linear operators. Written for researchers in operator theory, but also accessible to anyone with a reasonable background in functional analysis at the graduate level.
Linear Chaos
It is commonly believed that chaos is linked to non-linearity, however many (even quite natural) linear dynamical systems exhibit chaotic behavior. The study of these systems is a young and remarkably active field of research, which has seen many landmark results over the past two decades. Linear dynamics lies at the crossroads of several areas of mathematics including operator theory, complex analysis, ergodic theory and partial differential equations. At the same time its basic ideas can be easily understood by a wide audience. Written by two renowned specialists, Linear Chaos provides a welcome introduction to this theory. Split into two parts, part I presents a self-contained introductio...
Linear Dynamical Systems on Hilbert Spaces: Typical Properties and Explicit Examples
We solve a number of questions pertaining to the dynamics of linear operators on Hilbert spaces, sometimes by using Baire category arguments and sometimes by constructing explicit examples. In particular, we prove the following results. (i) A typical hypercyclic operator is not topologically mixing, has no eigen-values and admits no non-trivial invariant measure, but is densely distri-butionally chaotic. (ii) A typical upper-triangular operator with coefficients of modulus 1 on the diagonal is ergodic in the Gaussian sense, whereas a typical operator of the form “diagonal with coefficients of modulus 1 on the diagonal plus backward unilateral weighted shift” is ergodic but has only count...
Advanced Courses Of Mathematical Analysis Vi - Proceedings Of The Sixth International School
This volume contains short courses and recent papers by several specialists in different fields of Mathematical Analysis. It offers a wide perspective of the current state of research, and new trends, in areas related to Geometric Analysis, Harmonic Analysis, Complex Analysis, Functional Analysis and History of Mathematics. The contributions are presented with a remarkable expository nature and this makes the discussed topics accessible to a more general audience.
Open Problems in the Geometry and Analysis of Banach Spaces
This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help in convincing young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the tex...
Normative Economics in the History of Economic Thought
This book examines the role of normative economics in the writings of Karl Marx, Ludwig von Mises, Milton Friedman and Karl Popper. The book shows that while distinguishing positive from normative economics can be helpful, this distinction should not minimize the importance of normative economics or reject the possibility of offering objective evaluations of social phenomena and policies in normative economics. The book offers a critical assessment of the attempts by Marx, Mises and Friedman to reduce scientific economics to the positive analysis of social phenomena alone. Through a meticulous analysis of their work, the book shows that their positive theories fail to justify their evaluatio...
Advanced Courses of Mathematical Analysis II
This volume comprises a collection of articles by leading researchers in mathematical analysis. It provides the reader with an extensive overview of new directions and advances in topics for current and future research in the field.
The Diabetic Pancreas
Since the publication of the first edition of The Diabetic Pancreas in 1977, much progress has been made in various areas of diabetes research. While only a rela tively short while ago diabetes was considered a single disease, in more recent years it has become apparent that it is a heterogeneous group of disorders, all of which are characterized by a decreased tolerance of carbohydrates and most of which have a genetic basis, although the genetic types vary. In more recent years, an International Work Group sponsored by the National Diabetes Data Group of the NIH proposed a now generally accepted classification, according to which the insulin-dependent ketosis-prone diabetes, formerly and i...
