|
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNISA996418253103316 |
|
|
Autore |
Borthwick David |
|
|
Titolo |
Spectral Theory [[electronic resource] ] : Basic Concepts and Applications / / by David Borthwick |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Edizione |
[1st ed. 2020.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (X, 338 p. 31 illus., 30 illus. in color.) |
|
|
|
|
|
|
Collana |
|
Graduate Texts in Mathematics, , 0072-5285 ; ; 284 |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Partial differential equations |
Operator theory |
Functional analysis |
Partial Differential Equations |
Operator Theory |
Functional Analysis |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Nota di bibliografia |
|
Includes bibliographical references and index. |
|
|
|
|
|
|
Nota di contenuto |
|
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. |
|
|
|
|
|
|
|
|
Sommario/riassunto |
|
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. |
|
|
|
|
|
| |