04008nam 22006015 450 99641825310331620210419112254.03-030-38002-510.1007/978-3-030-38002-1(CKB)4100000010672229(DE-He213)978-3-030-38002-1(MiAaPQ)EBC6134084(Au-PeEL)EBL6134084(OCoLC)1145600259(PPN)243225830(EXLCZ)99410000001067222920210419d2020 uy 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierSpectral Theory[electronic resource] Basic Concepts and Applications /by David Borthwick1st ed. 2020.Cham :Springer International Publishing :Imprint: Springer,2020.1 online resource (X, 338 p. 31 illus., 30 illus. in color.)Graduate Texts in Mathematics,0072-5285 ;2843-030-38001-7 Includes bibliographical references and index.1. Introduction -- 2. Hilbert Spaces -- 3. Operators -- 4. Spectrum and Resolvent -- 5. The Spectral Theorem -- 6. The Laplacian with Boundary Conditions -- 7. Schrödinger Operators -- 8. Operators on Graphs -- 9. Spectral Theory on Manifolds -- A. Background Material -- References -- Index.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.Graduate Texts in Mathematics,0072-5285 ;284Partial differential equationsOperator theoryFunctional analysisPartial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Operator Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12139Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Partial differential equations.Operator theory.Functional analysis.Partial Differential Equations.Operator Theory.Functional Analysis.515.353Borthwick Davidauthttp://id.loc.gov/vocabulary/relators/aut503022MiAaPQMiAaPQMiAaPQBOOK996418253103316Spectral Theory2220278UNISA