Infinite-dimensional spectral computations : foundations, algorithms, and modern applications / Matthew J. Colbrook

Format:

Book

Author/Creator:

Colbrook, Matthew J., author.

Language:

English

Subjects (All):

Differential equations--Data processing.

Differential equations.

Differential equations, Partial--Data processing.

Differential equations, Partial.

Mathematical optimization.

System analysis.

Systems Analysis.

systems analysis.

Medical Subjects:

Systems Analysis.

Physical Description:

1 online resource

Place of Publication:

Cambridge : Cambridge University Press, 2026

Summary:

"Mathematicians, physicists, engineers, and data scientists will welcome this comprehensive, rigorous, and practical guide to computing spectral properties of operators in infinite-dimensional settings. It explains why standard discretisation can fail and shows how to overcome these pitfalls. It develops resolvent-based algorithms with provable convergence and certified error bounds, organised by a precise computability classification that clarifies what is achievable, what is impossible, and what extra information makes problems tractable. Topics include spectra and pseudospectra, spectral measures and functional calculus, spectral types, fractal and Cantor-type spectra, essential versus discrete spectra and multiplicities, spectral radii, abscissas and gaps, nonlinear operator pencils, and verified computation. A distinctive feature is the integration of modern applications, including a fully rigorous treatment of data-driven Koopman spectral analysis. Hundreds of worked examples, exercises with solutions, notes, and usable code make the book both a reference and a powerful toolkit for researchers and students"-- Provided by publisher

Contents:

Spectral problems in infinite dimensions

The solvability complexity index: a toolkit for classifying problems

Computing spectra with error control

Spectral measures of self-adjoint operators

Spectral measures of unitary operators

Spectral types of self-adjoint and unitary operators

Quantifying the size of spectra

Essential spectra

Spectral radii, abscissas, and gaps

Nonlinear spectral problems

Data-driven Koopman spectral problems for nonlinear dynamical systems

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (Cambridge Core, viewed August 5, 2026)

Other Format:

Print version: Colbrook, Matthew J. Infinite-dimensional spectral computations

ISBN:

9781009382502

1009382500

OCLC:

1570864622

Publisher Number:

CIPO000401425

Access Restriction:

Restricted for use by site license