LEADER 04008nam 22006015 450 001 996418253103316 005 20210419112254.0 010 $a3-030-38002-5 024 7 $a10.1007/978-3-030-38002-1 035 $a(CKB)4100000010672229 035 $a(DE-He213)978-3-030-38002-1 035 $a(MiAaPQ)EBC6134084 035 $a(Au-PeEL)EBL6134084 035 $a(OCoLC)1145600259 035 $a(PPN)243225830 035 $a(EXLCZ)994100000010672229 100 $a20210419d2020 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSpectral Theory$b[electronic resource] $eBasic Concepts and Applications /$fby David Borthwick 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (X, 338 p. 31 illus., 30 illus. in color.) 225 1 $aGraduate Texts in Mathematics,$x0072-5285 ;$v284 311 $a3-030-38001-7 320 $aIncludes bibliographical references and index. 327 $a1. 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. 330 $aThis textbook offers a concise introduction to spectral theory, designed for newcomers to functional analysis. Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas, exploring key examples in detail. Readers looking to delve further into specialized topics will find ample references to classic and recent literature. Beginning with a brief introduction to functional analysis, the text focuses on unbounded operators and separable Hilbert spaces as the essential tools needed for the subsequent theory. A thorough discussion of the concepts of spectrum and resolvent follows, leading to a complete proof of the spectral theorem for unbounded self-adjoint operators. Applications of spectral theory to differential operators comprise the remaining four chapters. These chapters introduce the Dirichlet Laplacian operator, Schrödinger operators, operators on graphs, and the spectral theory of Riemannian manifolds. Spectral Theory offers a uniquely accessible introduction to ideas that invite further study in any number of different directions. A background in real and complex analysis is assumed; the author presents the requisite tools from functional analysis within the text. This introductory treatment would suit a functional analysis course intended as a pathway to linear PDE theory. Independent later chapters allow for flexibility in selecting applications to suit specific interests within a one-semester course. 410 0$aGraduate Texts in Mathematics,$x0072-5285 ;$v284 606 $aPartial differential equations 606 $aOperator theory 606 $aFunctional analysis 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 615 0$aPartial differential equations. 615 0$aOperator theory. 615 0$aFunctional analysis. 615 14$aPartial Differential Equations. 615 24$aOperator Theory. 615 24$aFunctional Analysis. 676 $a515.353 700 $aBorthwick$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut$0503022 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418253103316 996 $aSpectral Theory$92220278 997 $aUNISA