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Unbounded Linear Operators: Theory and Applications (Dover Books on Mathematics), by Seymour Goldberg, Mathematics
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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.
- Sales Rank: #2877060 in Books
- Published on: 2006-08-04
- Released on: 2006-08-04
- Original language: English
- Number of items: 1
- Dimensions: 8.50" h x .45" w x 5.42" l, .53 pounds
- Binding: Paperback
- 208 pages
Most helpful customer reviews
11 of 11 people found the following review helpful.
Excellent complement to usual operator theory texts
By Bernardo Vargas
Most texts on functional analysis (linear operator theory) deal almost exclusively with bounded, or continuous, operators. However, when one studies some problems on differential equations one needs to work with unbounded operators.
This book constitutes a good starting point to get acquainted with such operators, mostly with closed and strictly singular ones. It includes some applications to perturbation theory and ordinary differential equations, and gives some comments on the Dirichlet problem for PDE's. Finally, its extensive list of references motivates you to deeper study.
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