Introduction to the Theory of Linear Nonselfadjoint Operators
Author: Israel Gohberg
Publisher: American Mathematical Soc.
Published: 1978
Total Pages: 402
ISBN-13: 9780821886502
DOWNLOAD EBOOK →Author: Israel Gohberg
Publisher: American Mathematical Soc.
Published: 1978
Total Pages: 402
ISBN-13: 9780821886502
DOWNLOAD EBOOK →Author: I. C. Gohberg
Publisher:
Published: 1969
Total Pages: 399
ISBN-13: 9781470444365
DOWNLOAD EBOOK →Author: Izrail Tsudikovich Gokhberg
Publisher:
Published: 1969
Total Pages: 378
ISBN-13:
DOWNLOAD EBOOK →Author: Izrailʹ T︠S︡udikovich Gokhberg
Publisher:
Published: 1969
Total Pages: 378
ISBN-13:
DOWNLOAD EBOOK →Author: M.S. Livsic
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 329
ISBN-13: 940158561X
DOWNLOAD EBOOK →Considering integral transformations of Volterra type, F. Riesz and B. Sz.-Nagy no ticed in 1952 that [49]: "The existence of such a variety of linear transformations, having the same spectrum concentrated at a single point, brings out the difficulties of characterization of linear transformations of general type by means of their spectra." Subsequently, spectral analysis has been developed for different classes of non selfadjoint operators [6,7,14,20,21,36,44,46,54]. It was then realized that this analysis forms a natural basis for the theory of systems interacting with the environment. The success of this theory in the single operator case inspired attempts to create a general theory in the much more complicated case of several commuting operators with finite-dimensional imaginary parts. During the past 10-15 years such a theory has been developed, yielding fruitful connections with algebraic geometry and sys tem theory. Our purpose in this book is to formulate the basic problems appearing in this theory and to present its main results. It is worth noting that, in addition to the joint spectrum, the corresponding algebraic variety and its global topological characteristics play an important role in the classification of commuting operators. For the case of a pair of operators these are: 1. The corresponding algebraic curve, and especially its genus. 2. Certain classes of divisors - or certain line bundles - on this curve.
Author: Seymour Goldberg
Publisher: Courier Corporation
Published: 2006-01-01
Total Pages: 212
ISBN-13: 0486453316
DOWNLOAD EBOOK →This volume presents a systematic treatment of the theory of unbounded linear operators in normed linear spaces with applications to differential equations. Largely self-contained, it is suitable for advanced undergraduates and graduate students, and it only requires a familiarity with metric spaces and real variable theory. After introducing the elementary theory of normed linear spaces--particularly Hilbert space, which is used throughout the book--the author develops the basic theory of unbounded linear operators with normed linear spaces assumed complete, employing operators assumed closed only when needed. Other topics include strictly singular operators; operators with closed range; perturbation theory, including some of the main theorems that are later applied to ordinary differential operators; and the Dirichlet operator, in which the author outlines the interplay between functional analysis and "hard" classical analysis in the study of elliptic partial differential equations. In addition to its readable style, this book's appeal includes numerous examples and motivations for certain definitions and proofs. Moreover, it employs simple notation, eliminating the need to refer to a list of symbols.