An Introduction to the Theory of Multipliers
An Introduction to the Theory of Multipliers

Author: Ronald Larsen

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 304

ISBN-13: 3642650309

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When I first considered writing a book about multipliers, it was my intention to produce a moderate sized monograph which covered the theory as a whole and which would be accessible and readable to anyone with a basic knowledge of functional and harmonic analysis. I soon realized, however, that such a goal could not be attained. This realization is apparent in the preface to the preliminary version of the present work which was published in the Springer Lecture Notes in Mathematics, Volume 105, and is even more acute now, after the revision, expansion and emendation of that manuscript needed to produce the present volume. Consequently, as before, the treatment given in the following pages is eclectric rather than definitive. The choice and presentation of the topics is certainly not unique, and reflects both my personal preferences and inadequacies, as well as the necessity of restricting the book to a reasonable size. Throughout I have given special emphasis to the func tional analytic aspects of the characterization problem for multipliers, and have, generally, only presented the commutative version of the theory. I have also, hopefully, provided too many details for the reader rather than too few.

The Keynesian Multiplier
The Keynesian Multiplier

Author: Claude Gnos

Publisher: Routledge

Published: 2008-05-25

Total Pages: 398

ISBN-13: 1134361939

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The multiplier is a central concept in Keynesian and post-Keynesian economics. It is largely what justifies activist full-employment fiscal policy: an increase in fiscal expenditures contributing to multiple rounds of spending, thereby financing itself. Yet, while a copingstone of post-Keynesian theory, it is not universally accepted by

Fredholm and Local Spectral Theory, with Applications to Multipliers
Fredholm and Local Spectral Theory, with Applications to Multipliers

Author: Pietro Aiena

Publisher: Springer Science & Business Media

Published: 2007-05-08

Total Pages: 452

ISBN-13: 1402025254

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A signi?cant sector of the development of spectral theory outside the classical area of Hilbert space may be found amongst at multipliers de?ned on a complex commutative Banach algebra A. Although the general theory of multipliers for abstract Banach algebras has been widely investigated by several authors, it is surprising how rarely various aspects of the spectral theory, for instance Fredholm theory and Riesz theory, of these important classes of operators have been studied. This scarce consideration is even more surprising when one observes that the various aspects of spectral t- ory mentioned above are quite similar to those of a normal operator de?ned on a complex Hilbert space. In the last ten years the knowledge of the spectral properties of multip- ers of Banach algebras has increased considerably, thanks to the researches undertaken by many people working in local spectral theory and Fredholm theory. This research activity recently culminated with the publication of the book of Laursen and Neumann [214], which collects almost every thing that is known about the spectral theory of multipliers.

Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers
Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

Author: Stephen Boyd

Publisher: Now Publishers Inc

Published: 2011

Total Pages: 138

ISBN-13: 160198460X

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Surveys the theory and history of the alternating direction method of multipliers, and discusses its applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others.

An Introduction to Local Spectral Theory
An Introduction to Local Spectral Theory

Author: K. B. Laursen

Publisher: Oxford University Press

Published: 2000

Total Pages: 610

ISBN-13: 9780198523819

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Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces. This book provides an in-depth introduction to the natural expansion of this fascinating topic of Banach space operator theory. It gives complete coverage of the field, including the fundamental recent work by Albrecht and Eschmeier which provides the full duality theory for Banach space operators. One of its highlights are the many characterizations of decomposable operators, and of other related, important classes of operators, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity. Written in a careful and detailed style, it contains numerous examples, many simplified proofs of classical results, extensive references, and open problems, suitable for continued research.

Local Multipliers of C*-Algebras
Local Multipliers of C*-Algebras

Author: Pere Ara

Publisher: Springer Science & Business Media

Published: 2002-10-07

Total Pages: 346

ISBN-13: 9781852332372

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Many problems in operator theory lead to the consideration ofoperator equa tions, either directly or via some reformulation. More often than not, how ever, the underlying space is too 'small' to contain solutions of these equa tions and thus it has to be 'enlarged' in some way. The Berberian-Quigley enlargement of a Banach space, which allows one to convert approximate into genuine eigenvectors, serves as a classical example. In the theory of operator algebras, a C*-algebra A that turns out to be small in this sense tradition ally is enlarged to its (universal) enveloping von Neumann algebra A". This works well since von Neumann algebras are in many respects richer and, from the Banach space point of view, A" is nothing other than the second dual space of A. Among the numerous fruitful applications of this principle is the well-known Kadison-Sakai theorem ensuring that every derivation 8 on a C*-algebra A becomes inner in A", though 8 may not be inner in A. The transition from A to A" however is not an algebraic one (and cannot be since it is well known that the property of being a von Neumann algebra cannot be described purely algebraically). Hence, ifthe C*-algebra A is small in an algebraic sense, say simple, it may be inappropriate to move on to A". In such a situation, A is typically enlarged by its multiplier algebra M(A).

How Big (Small?) are Fiscal Multipliers?
How Big (Small?) are Fiscal Multipliers?

Author: Ethan Ilzetzki

Publisher: International Monetary Fund

Published: 2011-03-01

Total Pages: 68

ISBN-13: 1455218022

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We contribute to the intense debate on the real effects of fiscal stimuli by showing that the impact of government expenditure shocks depends crucially on key country characteristics, such as the level of development, exchange rate regime, openness to trade, and public indebtedness. Based on a novel quarterly dataset of government expenditure in 44 countries, we find that (i) the output effect of an increase in government consumption is larger in industrial than in developing countries, (ii) the fisscal multiplier is relatively large in economies operating under predetermined exchange rate but zero in economies operating under flexible exchange rates; (iii) fiscal multipliers in open economies are lower than in closed economies and (iv) fiscal multipliers in high-debt countries are also zero.

Littlewood-Paley and Multiplier Theory
Littlewood-Paley and Multiplier Theory

Author: R. E. Edwards

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 223

ISBN-13: 3642663664

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This book is intended to be a detailed and carefully written account of various versions of the Littlewood-Paley theorem and of some of its applications, together with indications of its general significance in Fourier multiplier theory. We have striven to make the presentation self-contained and unified, and adapted primarily for use by graduate students and established mathematicians who wish to begin studies in these areas: it is certainly not intended for experts in the subject. It has been our experience, and the experience of many of our students and colleagues, that this is an area poorly served by existing books. Their accounts of the subject tend to be either ill-suited to the needs of a beginner, or fragmentary, or, in one or two instances, obscure. We hope that our book will go some way towards filling this gap in the literature. Our presentation of the Littlewood-Paley theorem proceeds along two main lines, the first relating to singular integrals on locally com pact groups, and the second to martingales. Both classical and modern versions of the theorem are dealt with, appropriate to the classical n groups IRn, ?L , Tn and to certain classes of disconnected groups. It is for the disconnected groups of Chapters 4 and 5 that we give two separate accounts of the Littlewood-Paley theorem: the first Fourier analytic, and the second probabilistic.