Live briefing
Everything about Spectrum (functional analysis)
Set of eigenvalues of a matrix
In mathematics, particularly in functional analysis, the spectrum of a bounded linear operator is a generalisation of the set of eigenvalues of a matrix. Specifically, a complex number is said to be in the spectrum of a bounded linear operator ifeither has no set-theoretic inverse; or the set-theoretic inverse is either unbounded or defined on a non-dense subset. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Spectrum (functional analysis)A 5-minute orientation
- Skim a recent paper: Systematic review and meta-analysis: multimodal functional and anatomical neural alterations in autism spectrum disorderInfluential work since 2022
- Pick up a classic book: Equivalent widths of isolated Lorentz & Doppler lines and miscellaneous exponential functionsThe most-reprinted book on the subject
- Read the landmark paper: Developmental Meta-Analysis of the Functional Neural Correlates of Autism Spectrum DisordersCited 68 times
- Go sideways: Decomposition of spectrum (functional analysis)A closely related topic
- Go sideways: Discrete spectrum (mathematics)A closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Developmental Meta-Analysis of the Functional Neural Correlates of Autism Spectrum Disorders
Classification of Autism Spectrum Disorder From EEG-Based Functional Brain Connectivity Analysis
Functional analysis of gut microbiota and immunoinflammation in children with autism spectrum disorders
Functional Analysis Helps to Define KCNC3 Mutational Spectrum in Dutch Ataxia Cases
SINGULAR SPECTRUM ANALYSIS AND ADAPTIVE FILTERING ENHANCE THE FUNCTIONAL CONNECTIVITY ANALYSIS OF RESTING STATE fMRI DATA
Functional singular spectrum analysis
Identification and Functional Analysis of Long Non-coding RNAs in Autism Spectrum Disorders
Stability of singularly perturbed functional-differential systems: spectrum analysis and LMI approaches
🆕 Influential since 2022
Systematic review and meta-analysis: multimodal functional and anatomical neural alterations in autism spectrum disorder
Resting state EEG power spectrum and functional connectivity in autism: a cross-sectional analysis
Edge-centric analysis of time-varying functional brain networks with applications in autism spectrum disorder
The Puzzle of Functional Recovery in Schizophrenia-Spectrum Disorders—Replicating a Network Analysis Study
Identification and analysis of autism spectrum disorder via large‐scale dynamic functional network connectivity
📚 Books worth reading
Equivalent widths of isolated Lorentz & Doppler lines and miscellaneous exponential functionsStanley Golden · 1968
Maximum-Entropy and Bayesian Methods in Inverse ProblemsC. Ray Smith, Walter T. Grandy · 1985- 📕Green functions and pressure broadening problemsJamal Manassah · 1970
- 📕Symmetry, spectroscopy and SCHURProfessor Brian G. Wybourne Commemorative Meeting (2005 Toruń, Poland) · 2006
- 📕Random fields and stochastic Lagrangian modelsK. K. Sabelʹfelʹd · 2013
- 📕An improved quasistatic line-shape theoryQ. Ma · 1994
Quantum kinetics in transport and optics of semiconductorsHartmut Haug, Antti-Pekka Jauho · 2007- 📕Geometric and spectral analysisPierre Albin, Dmitry Jakobson · 2014
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Decomposition of spectrum (functional analysis) The spectrum of a linear operator T that operates on a Banach space X is a fundamental concept of functional analysis. The spectrum consists of all scalars…
- Discrete spectrum (mathematics) In mathematics, specifically in spectral theory, a discrete spectrum of a closed linear operator is defined as the set of isolated points of its spectrum…
- Essential spectrum In mathematics, the essential spectrum of a bounded operator (or, more generally, of a densely defined closed linear operator) is a certain subset of its…
- Unilateral shift operator In operator theory, the unilateral shift is a one-sided shift operator, that is, a shift operator acting on one-sided sequences or shift spaces. The term…
- Compact operator In functional analysis, a branch of mathematics, a compact operator is a linear operator that behaves, in several important respects, like a finite-dimensional…
- Spectral theory In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader…
- Compact operator on Hilbert space In the mathematical discipline of functional analysis, the concept of a compact operator on Hilbert space is an extension of the concept of a matrix acting…
- Spectral theory of ordinary differential equations In mathematics, the spectral theory of ordinary differential equations is the part of spectral theory concerned with the determination of the spectrum…