| 000 | 02194 a2200229 4500 | ||
|---|---|---|---|
| 003 | OSt | ||
| 005 | 20250106120501.0 | ||
| 008 | 250103b xxu||||| |||| 00| 0 eng d | ||
| 020 | _a9783030380014 | ||
| 040 | _cIIT Kanpur | ||
| 041 | _aeng | ||
| 082 |
_a515.7222 _bB648s |
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| 100 | _aBorthwick, David | ||
| 245 |
_aSpectral theory _bbasic concepts and applications _cDavid Borthwick |
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| 260 |
_bSpringer _c2020 _aSwitzerland |
||
| 300 | _ax, 338p | ||
| 440 | _aGraduate texts mathematics | ||
| 490 |
_a/ edited by Sheldon Axler and Kenneth Ribet _v; n. 284 |
||
| 520 | _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. | ||
| 650 | _aSpectral theory (Mathematics) | ||
| 942 | _cBK | ||
| 999 |
_c567319 _d567319 |
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