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Spectral Theory: Basic Concepts and Applications (Graduate Texts in Mathematics, 284) - Hardcover

 
9783030380014: Spectral Theory: Basic Concepts and Applications (Graduate Texts in Mathematics, 284)
  • PublisherSpringer
  • Publication date2020
  • ISBN 10 3030380017
  • ISBN 13 9783030380014
  • BindingHardcover
  • LanguageEnglish
  • Number of pages348

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9783030380045: Spectral Theory: Basic Concepts and Applications (Graduate Texts in Mathematics, 284)

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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This textbook offers a concise introduction to spectral theory, designed for newcomers to functional analysis. Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas, exploring key examples in detail. Readers looking to delve further into specialized topics will find ample references to classic and recent literature.Beginning with a brief introduction to functional analysis, the text focuses on unbounded operators and separable Hilbert spaces as the essential tools needed for the subsequent theory. A thorough discussion of the concepts of spectrum and resolvent follows, leading to a complete proof of the spectral theorem for unbounded self-adjoint operators. Applications of spectral theory to differential operators comprise the remaining four chapters. These chapters introduce the Dirichlet Laplacian operator, Schrödinger operators, operators on graphs, and the spectral theory of Riemannian manifolds.Spectral Theory offers a uniquely accessible introduction to ideas that invite further study in any number of different directions. A background in real and complex analysis is assumed; the author presents the requisite tools from functional analysis within the text. This introductory treatment would suit a functional analysis course intended as a pathway to linear PDE theory. Independent later chapters allow for flexibility in selecting applications to suit specific interests within a one-semester course. 348 pp. Englisch. Seller Inventory # 9783030380014

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