Functional Analysis

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Includes sections on the spectral resolution and spectralrepresentation of self adjoint operators, invariant subspaces,strongly continuous one-parameter semigroups, the index ofoperators, the trace formula of Lidskii, the Fredholm determinant,and more.
* Assumes prior knowledge of Naive set theory, linear algebra,point set topology, basic complex variable, and realvariables.
* Includes an appendix on the Riesz representation theorem.
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Additional Information

Publisher
John Wiley & Sons
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Published on
Aug 28, 2014
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Pages
608
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ISBN
9781118626740
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Language
English
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Genres
Mathematics / Functional Analysis
Mathematics / Mathematical Analysis
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Content Protection
This content is DRM protected.
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Praise for the First Edition

". . .recommended for the teacher and researcher as well as forgraduate students. In fact, [it] has a place on everymathematician's bookshelf." -American Mathematical Monthly

Linear Algebra and Its Applications, Second Edition presents linearalgebra as the theory and practice of linear spaces and linear mapswith a unique focus on the analytical aspects as well as thenumerous applications of the subject. In addition to thoroughcoverage of linear equations, matrices, vector spaces, game theory,and numerical analysis, the Second Edition featuresstudent-friendly additions that enhance the book's accessibility,including expanded topical coverage in the early chapters,additional exercises, and solutions to selected problems.

Beginning chapters are devoted to the abstract structure of finitedimensional vector spaces, and subsequent chapters addressconvexity and the duality theorem as well as describe the basics ofnormed linear spaces and linear maps between normed spaces.

Further updates and revisions have been included to reflect themost up-to-date coverage of the topic, including: The QR algorithm for finding the eigenvalues of a self-adjointmatrix
The Householder algorithm for turning self-adjoint matricesinto tridiagonal formThe compactness of the unit ball as a criterion of finitedimensionality of a normed linear spaceAdditionally, eight new appendices have been added and cover topicssuch as: the Fast Fourier Transform; the spectral radius theorem;the Lorentz group; the compactness criterion for finitedimensionality; the characterization of commentators; proof ofLiapunov's stability criterion; the construction of the JordanCanonical form of matrices; and Carl Pearcy's elegant proof ofHalmos' conjecture about the numerical range of matrices.

Clear, concise, and superbly organized, Linear Algebra and ItsApplications, Second Edition serves as an excellent text foradvanced undergraduate- and graduate-level courses in linearalgebra. Its comprehensive treatment of the subject also makes itan ideal reference or self-study for industry professionals.
Richard Silverman's new translation makes available to English readers the work of the famous contemporary Russian mathematician N. N. Lebedev. Though extensive treatises on special functions are available, these do not serve the student or the applied mathematician as well as Lebedev's introductory and practically oriented approach. His systematic treatment of the basic theory of the more important special functions and the applications of this theory to specific problems of physics and engineering results in a practical course in the use of special functions for the student and for those concerned with actual mathematical applications or uses. In consideration of the practical nature of the coverage, most space has been devoted to the application of cylinder functions and particularly of spherical harmonics. Lebedev, however, also treats in some detail: the gamma function, the probability integral and related functions, the exponential integral and related functions, orthogonal polynomials with consideration of Legendre, Hermite and Laguerre polynomials (with exceptional treatment of the technique of expanding functions in series of Hermite and Laguerre polynomials), the Airy functions, the hypergeometric functions (making this often slighted area accessible to the theoretical physicist), and parabolic cylinder functions. The arrangement of the material in the separate chapters, to a certain degree, makes the different parts of the book independent of each other. Although a familiarity with complex variable theory is needed, a serious attempt has been made to keep to a minimum the required background in this area. Various useful properties of the special functions which do not appear in the text proper will be found in the problems at the end of the appropriate chapters. This edition closely adheres to the revised Russian edition (Moscow, 1965). Richard Silverman, however, has made the book even more useful to the English reader. The bibliography and references have been slanted toward books available in English or the West European languages, and a number of additional problems have been added to this edition.
Praise for the First Edition

". . .recommended for the teacher and researcher as well as forgraduate students. In fact, [it] has a place on everymathematician's bookshelf." -American Mathematical Monthly

Linear Algebra and Its Applications, Second Edition presents linearalgebra as the theory and practice of linear spaces and linear mapswith a unique focus on the analytical aspects as well as thenumerous applications of the subject. In addition to thoroughcoverage of linear equations, matrices, vector spaces, game theory,and numerical analysis, the Second Edition featuresstudent-friendly additions that enhance the book's accessibility,including expanded topical coverage in the early chapters,additional exercises, and solutions to selected problems.

Beginning chapters are devoted to the abstract structure of finitedimensional vector spaces, and subsequent chapters addressconvexity and the duality theorem as well as describe the basics ofnormed linear spaces and linear maps between normed spaces.

Further updates and revisions have been included to reflect themost up-to-date coverage of the topic, including: The QR algorithm for finding the eigenvalues of a self-adjointmatrix
The Householder algorithm for turning self-adjoint matricesinto tridiagonal formThe compactness of the unit ball as a criterion of finitedimensionality of a normed linear spaceAdditionally, eight new appendices have been added and cover topicssuch as: the Fast Fourier Transform; the spectral radius theorem;the Lorentz group; the compactness criterion for finitedimensionality; the characterization of commentators; proof ofLiapunov's stability criterion; the construction of the JordanCanonical form of matrices; and Carl Pearcy's elegant proof ofHalmos' conjecture about the numerical range of matrices.

Clear, concise, and superbly organized, Linear Algebra and ItsApplications, Second Edition serves as an excellent text foradvanced undergraduate- and graduate-level courses in linearalgebra. Its comprehensive treatment of the subject also makes itan ideal reference or self-study for industry professionals.
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