Spectral Theory

Spectral Theory: Basic Concepts and Applications introduces spectral principles to readers beginning their study of functional analysis. The textbook presents foundational operator methods while serving as an introductory pathway toward linear partial differential equations.

The text develops core tools in functional analysis, focusing on separable Hilbert spaces and unbounded operators. Detailed treatment of spectra and resolvents establishes the groundwork needed to construct a complete proof of the spectral theorem for unbounded self-adjoint operators.

Assuming a background in real and complex analysis, the volume builds requisite functional analytic tools directly within the text. Independent chapters explore differential operators, addressing concrete settings such as Schrödinger operators and Dirichlet Laplacians.