Spectral Theory: Basic Concepts and Applications (PDF) offers a brief introduction to spectral theory, designed for newcomers to functional analysis. Curating the content wisely, the author builds a proof of the spectral theorem in the early part of the ebook. The following chapters illustrate a number of application areas, exploring important examples in detail. Readers looking to probe further into specialized topics will find plenty of references to classic and recent literature.
Starting with a brief introduction to functional analysis, the text concentrates on unbounded operators and separable Hilbert spaces as the vital tools needed for the subsequent theory. A thorough discussion of the models of spectrum and resolvent follows, leading to complete proof of the spectral theorem for immeasurable self-adjoint operators. Applications of spectral theory to differential operators include the remaining four chapters. These chapters introduce the Dirichlet Laplacian operator, operators on graphs, Schrödinger operators, and the spectral theory of Riemannian manifolds.
Spectral Theory provides a uniquely accessible introduction to ideas that invite further study in any number of different directions. A background in complex and real analysis is assumed; the author provides the requisite tools from functional analysis within the text. This introductory treatment would suit a functional analysis course aimed as a pathway to linear PDE theory. Independent later chapters allow for flexibility in selecting applications to suit particular interests within a one-semester course.
“This is an outstanding ebook, which shall be a very helpful tool for anyone who is oriented to the applications of functional analysis, particularly to partial differential equations.” — Panagiotis Koumantos
NOTE: The product only includes the ebook, Spectral Theory in PDF. No access codes are included.