Spectral theory : basic concepts and applications
By: Borthwick, David.
Series: Graduate texts mathematics. / edited by Sheldon Axler and Kenneth Ribet ; n. 284.Publisher: Switzerland Springer 2020Description: x, 338p.ISBN: 9783030380014.Subject(s): Spectral theory (Mathematics)DDC classification: 515.7222 | B648s Summary: 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.| Item type | Current location | Collection | Call number | Status | Date due | Barcode | Item holds |
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PK Kelkar Library, IIT Kanpur | On Display | 515.7222 B648s (Browse shelf) | Available | A186650 |
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| 514.2 Sch27a Algebraic foundations for applied topology and data analysis | 515.7 T871a Analysis and quantum groups | 515.7 W666f2 Functional analysis [2nd ed.] | 515.7222 B648s Spectral theory | 516.642 Su71s Stochastic linear-quadratic optimal control theory | 518 St49n Numerical analysis |
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.
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