Open AccessRepresentation of weakly harmonizable processes
Author(s) -
M. M. Rao
Publication year - 1981
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.78.9.5288
Subject(s) - hilbert space , mathematics , characterization (materials science) , pure mathematics , measure (data warehouse) , fourier transform , space (punctuation) , unitary state , representation (politics) , positive definite matrix , fourier analysis , mathematical analysis , physics , computer science , eigenvalues and eigenvectors , quantum mechanics , database , politics , law , political science , optics , operating system
Weakly harmonizable processes are represented by a family of positive definite contractive linear operators in a Hilbert space. This generalizes the known result on weakly stationary processes involving a unitary family. A characterization of the vector Fourier integral of a measure on R → [unk], a reflexive space, is given, and this yields another characterization of weakly harmonizable processes when [unk] is a Hilbert space. Also these processes are shown to have associated spectra, yielding a positive solution to a problem of Rozanov.