Szegő limit theorem

E451539

mathematical theorem result in analysis result in operator theory

The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.

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All labels observed (2)

Label	Occurrences
Szegő limit theorem canonical	1
Szegő limit theorem in analysis	1

Statements (49)

Predicate	Object
instanceOf	mathematical theorem ⓘ result in analysis ⓘ result in operator theory ⓘ
appliesTo	large Toeplitz matrices ⓘ
assumes	integrable symbol on the unit circle ⓘ nonvanishing symbol on the unit circle ⓘ
concerns	Toeplitz matrices NERFINISHED ⓘ Toeplitz operators NERFINISHED ⓘ asymptotic behavior of determinants ⓘ determinants of Toeplitz matrices ⓘ symbols of Toeplitz matrices ⓘ
describes	asymptotics of log determinants of Toeplitz matrices ⓘ
domain	infinite-dimensional analysis ⓘ spectral theory ⓘ
field	complex analysis ⓘ functional analysis ⓘ harmonic analysis ⓘ matrix analysis ⓘ operator theory ⓘ probability theory ⓘ
generalizationOf	strong law of large numbers for eigenvalue distributions of Toeplitz matrices ⓘ
hasFormulation	limit of (1/n) log det T_n(f) equals average of log f ⓘ
hasGeneralization	results for block Toeplitz matrices ⓘ results for multidimensional symbols ⓘ results for non-Hermitian Toeplitz matrices ⓘ
hasVariant	block Szegő limit theorem NERFINISHED ⓘ multidimensional Szegő limit theorem NERFINISHED ⓘ strong Szegő limit theorem NERFINISHED ⓘ weak Szegő limit theorem NERFINISHED ⓘ
historicalPeriod	20th century mathematics ⓘ
implies	asymptotic distribution of eigenvalues of Toeplitz matrices ⓘ
influenced	development of Toeplitz operator theory ⓘ
involves	integral of log of the symbol over the unit circle ⓘ limit of normalized log determinants ⓘ
languageOfOriginalPublication	German ⓘ
namedAfter	Gábor Szegő NERFINISHED ⓘ
relatedTo	Fisher–Hartwig conjecture NERFINISHED ⓘ Szegő–Kolmogorov formula NERFINISHED ⓘ Wiener–Hopf factorization NERFINISHED ⓘ prediction theory of stationary processes ⓘ
relates	determinants of Toeplitz matrices to integrals of their symbols ⓘ
usedIn	information theory ⓘ random matrix theory ⓘ signal processing ⓘ statistical mechanics ⓘ time series analysis ⓘ
usesConcept	Fourier coefficients ⓘ Fourier series NERFINISHED ⓘ logarithm of the symbol ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Gábor Szegő → notableWork → Szegő limit theorem ⓘ

Gábor Szegő → knownFor → Szegő limit theorem ⓘ

this entity surface form: Szegő limit theorem in analysis