Operators Books

It really shed light on some concepts that other books simply do not discuss. It is also the only one I know that gives a theoretical basis for understanding dimensional regularization.

This book and the journal papers that preceded it launched the new era of algebraic control theory which is one of the main new trends in mathematics, engineering, and physics. Control theory is just what is sounds like: control in the intuitive sense (usually of artificial satellites, rockets, robots, but also manufacturing and chemical plants, cars, physical and biological thermoregulatory systems, etc.). The old control theory lacked simplicity, clarity, organization, and even inspiration, and was done by long calculations with little algebraic time-saving or space-saving. Bruce Francis, whom the author cites and with whom the author collaborated earlier, began the search for time- and space-saving methods, although his own monograph makes difficult reading. Feintuch's book is crystal clear, organized, and time- and space-saving. He even isolates for us his main methods: not H-infinity but nest algebras and their operator theory framework which lead to a theory of uniform optimal control and robustness for time-varying linear systems, Arveson's distance formula based on operator matrices in algebra, internal stability representing a linear system as the range of 2x1 operator matrices with causal entries and stabilization corresponds to left causal invertibility, the gap metric, factorizations including inner-outer, spectral, coprime. Block matrices turn out to be very important. Feintuch's theory is mostly in Hilbert space rather than Banach space, although he introduces Banach algebras and does some work in Banach space. Hilbert space has been found to be defective in quantum theory by A. Bohm and was "repaired" by him by adding Hilbert and Banach lattices and rigged Hilbert spaces, but it is becoming obvious that a new direction is needed both in quantum theory and control theory: Banach spaces. My own work is in this latter area. I could have used Feintuch's insights when I worked in satellites for the U.S. Defense Department. The reader unfamiliar with the mathematics can hire a consultant or tutor to translate things into approximate English, an endeavor well worth the time and effort.

The next step after Vekua's, Muskhelishvili's and Gakhov's treatises on singular integrals and its applications is this thick encyclopedic volume.

Including most of the topics covered in the above-mentioned texts, the authors go further to present all of the important results plus some new ones in a unified way.

Contents: Basic Facts from Functional Analysis; The One-dimensional Singular Integral; One-dimensional Singular Integral Equations with Continuous Coefficients on Closed Curves; One-dimensional Singular Integral Equations with Discontinuous Coefficients; Systems of One-dimensional Singular Equations; One-dimensional Singular Equations with Degenerate Symbol; Some Problems Leading to Singular Integral Equations; Some Further Subsidiaries; Singular Integrals of Higher Dimensions in Spaces with a Uniform Metric; The Symbol of Higher Dimensional Singular Integral Operators; Singular Integral Operators in Spaces with Integral Metric; Multidimensional Singular Integral Equations; Singular Equations on Smooth Manifolds without Boundary; Systems of Multidimensional Singular Equations; The Localization Principle, Singular Operators on Manifolds with Boundary; Mutidimensional Singular Equations with Degenerate Symbol; Methods for the Approximate Solution of One-dimensional Singular Integral Equations; Approximate Solution of Multidimensional Singular Integral Equations. References.

The book is intended for experts but most parts could (and should) be covered in graduate courses.

Please take a look at the rest of my reviews.

California residents are well aware of headlines which reference the California Independent System Operator when speaking of energy grid issues, but SOUL OF THE GRID: A CULTURAL BIOGRAPHY OF HE CALIFORNIA INDEPENDENT SYSTEM OPERATOR is absolutely essential for understanding these news headline references. It probes the creation of California's power market, why the ISO was developed, and what happened during the power crisis of 200-2001. Chapters chart politics, California's electricity marketplace, key figures on all sides, and are essential for any educated discussion of the topic, making SOUL OF THE GRID a top pick for any California library, whether college-level or public lending institution.

Diane C. Donovan
California Bookwatch

From Back Cover:

To: New Astronauts

Welcome Aboard!

You are about to embark on a spectacular adventure, blazing a trail for future space travel in the world's greatest flying machine.

Prepare for lift-off using the step-by-step instructions for launch and ascent. Soar into the sky consulting the authentic gatefold reproduction of the Shuttle's instrument panel. Operate the remote manipulator arm, the space telescope, and the data rely satellite as you communicate with ground control. Chart your space flight using the authentic fold-out orbital map. Hurtle back through the Earth's atmosphere to land the aircraft gently, like a glider.

Congratulations! We hope your mission is rewarding and fascinating!

Sincerely,

Directorate for Crew Training

The authors present an exceptionally clear treatment of Clifford algebras, Clifford C*-algebras, and von Neumann Clifford algebras, their Fock representations and related developments. The proofs are concise and to the point.

The books "The Successful Truck Owner Operator" and " The Road To Financial Success" are selling for $14.95 at http://www.truckingsuccess.com and are the top of the line. Many reviews on the web site from thousands of customers are very positive. The review from a previous customer was intended to hurt the reputation of the author. Don't buy outdated books, the 2004 Editions are only available from www.truckingsuccess.com.

The book under review is a nice introduction into a currently very active area called Asymptotic (or Local) Theory of Normed Spaces. It contains such topics as nuclear and summing norms, trace duality, Grothendieck Theorem, type, cotype, and so on. One of the nice qualities of this book is that reading it one can learn some of the most powerful tools of the Asymptotic Theory in a couple of weeks. After reading this book beginners can turn to more advances books on the topic, such as books of V.D. Milman & G. Schechtman and G. Pisier.

peter l antonelli is one of the greatest mathematicians of all time, by reading this book, you have not only gained a great deal of knowledge... but have also taken in a part of this marvelous man....

PRAISE PETER L ANTONELLI!!!