Introduction to Optimization Theory in a Hilbert Space PDF Download

Author: A.V. Balakrishnan
Publisher: Springer Science & Business Media
ISBN: 3642960367
Category : Business & Economics
Languages : en
Pages : 162

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Book Description
This book is based on lectures given in a one-quarter course at UCLA. The aim. is to present som.e of the basic concepts and techniques of Functional Analys.is of relevance to optim.ization problem.s in Control. Com.m.unication and other areas in System. Science. The students are expected to have had an introductory course in Hilbert Space theory. Som.e effort has been m.ade to be self-contained m.ainly in order that the vocabularly used can be clarified. A m.inim.al bibliography is appended. The author is indebted to Jiri Ruzicka and Jerom.e Mersky for help with proof-reading. Profes sor L. Berkovitz looked over and m.ade m.any helpful corn.rn.ents on parts of an early version. Thanks are also due to Trudy Cook for typing the m.anuscript. Grateful acknowledgem.ent is also m.ade of partial support under AFOSR Grant No. 68-1408, Applied Mathem.atics Division, United Stat s Air Force.

Author: David G. Luenberger
Publisher: John Wiley & Sons
ISBN: 9780471181170
Category : Technology & Engineering
Languages : en
Pages : 348

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Book Description
Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.

Author: N. Young
Publisher: Cambridge University Press
ISBN: 1107717167
Category : Mathematics
Languages : en
Pages : 254

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Book Description
This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.

Author: Samia Challal
Publisher: CRC Press
ISBN: 0429511736
Category : Business & Economics
Languages : en
Pages : 335

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Book Description
Introduction to the Theory of Optimization in Euclidean Space is intended to provide students with a robust introduction to optimization in Euclidean space, demonstrating the theoretical aspects of the subject whilst also providing clear proofs and applications. Students are taken progressively through the development of the proofs, where they have the occasion to practice tools of differentiation (Chain rule, Taylor formula) for functions of several variables in abstract situations. Throughout this book, students will learn the necessity of referring to important results established in advanced Algebra and Analysis courses. Features Rigorous and practical, offering proofs and applications of theorems Suitable as a textbook for advanced undergraduate students on mathematics or economics courses, or as reference for graduate-level readers Introduces complex principles in a clear, illustrative fashion

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Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Author: Lokenath Debnath
Publisher: Elsevier
ISBN: 0080455921
Category : Mathematics
Languages : en
Pages : 599

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Book Description
Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular chapter on wavelets that has been completely updated. Students and researchers agree that this is the definitive text on Hilbert Space theory. - Updated chapter on wavelets - Improved presentation on results and proof - Revised examples and updated applications - Completely updated list of references

Author: Lokenath Debnath
Publisher: Academic Press
ISBN: 0122084381
Category : Mathematics
Languages : en
Pages : 600

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Book Description
"Continuing on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory complemented by a variety of applications. Students and researchers will benefit from the enhanced presentation of results and proofs and new and revised examples. A completely new section on Sobolev spaces has been added, and the treatment of finite dimensional normed spaces has been expanded. The chapter on wavelets has been updated."--BOOK JACKET.

Author: Carlos S. Kubrusly
Publisher: Springer Science & Business Media
ISBN: 9780817639921
Category : Mathematics
Languages : en
Pages : 152

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Book Description
By a Hilbert-space operator we mean a bounded linear transformation be tween separable complex Hilbert spaces. Decompositions and models for Hilbert-space operators have been very active research topics in operator theory over the past three decades. The main motivation behind them is the in variant subspace problem: does every Hilbert-space operator have a nontrivial invariant subspace? This is perhaps the most celebrated open question in op erator theory. Its relevance is easy to explain: normal operators have invariant subspaces (witness: the Spectral Theorem), as well as operators on finite dimensional Hilbert spaces (witness: canonical Jordan form). If one agrees that each of these (i. e. the Spectral Theorem and canonical Jordan form) is important enough an achievement to dismiss any further justification, then the search for nontrivial invariant subspaces is a natural one; and a recalcitrant one at that. Subnormal operators have nontrivial invariant subspaces (extending the normal branch), as well as compact operators (extending the finite-dimensional branch), but the question remains unanswered even for equally simple (i. e. simple to define) particular classes of Hilbert-space operators (examples: hyponormal and quasinilpotent operators). Yet the invariant subspace quest has certainly not been a failure at all, even though far from being settled. The search for nontrivial invariant subspaces has undoubtly yielded a lot of nice results in operator theory, among them, those concerning decompositions and models for Hilbert-space operators. This book contains nine chapters.

Author: Ralph E. Showalter
Publisher: Courier Corporation
ISBN: 0486135799
Category : Mathematics
Languages : en
Pages : 226

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Book Description
This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.

Author: Alampallam V. Balakrishnan
Publisher: Springer Science & Business Media
ISBN: 1461258650
Category : Mathematics
Languages : en
Pages : 385

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Book Description
In preparing the second edition, I have taken advantage of the opportunity to correct errors as well as revise the presentation in many places. New material has been included, in addition, reflecting relevant recent work. The help of many colleagues (and especially Professor J. Stoer) in ferreting out errors is gratefully acknowledged. I also owe special thanks to Professor v. Sazonov for many discussions on the white noise theory in Chapter 6. February, 1981 A. V. BALAKRISHNAN v Preface to the First Edition The title "Applied Functional Analysis" is intended to be short for "Functional analysis in a Hilbert space and certain of its applications," the applications being drawn mostly from areas variously referred to as system optimization or control systems or systems analysis. One of the signs of the times is a discernible tilt toward application in mathematics and conversely a greater level of mathematical sophistication in the application areas such as economics or system science, both spurred undoubtedly by the heightening pace of digital computer usage. This book is an entry into this twilight zone. The aspects of functional analysis treated here are rapidly becoming essential in the training at the advance graduate level of system scientists and/or mathematical economists. There are of course now available many excellent treatises on functional analysis.