Abstract
A very short proof of the Fejér-Riesz lemma is presented in the matrix case.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Barclay, S.: Continuity of the spectral factorization mapping. J. Lond. Math. Soc. (2) 70, 763–779 (2004)
Ephremidze, L., Janashia, G., Lagvilava, E.: A new efficient matrix spectral factorization algorithm. In: Proceedings of the SICE Annual Conference, Kagawa University, Japan (2007)
Ephremidze, L., Janashia, G., Lagvilava, E.: An analytic proof of the matrix spectral factorization theorem. Georgian Math. J. 15, 241–249 (2008)
Hardin, D.P., Hogan, T.A., Sun, Q.: The matrix-valued Riesz lemma and local orthonormal bases in shift-invariant spaces. Adv. Comput. Math. 20, 367–384 (2004)
Helson, H.: Lectures on Invariant Subspaces. Academic, San Diego (1964)
Helson, H., Lowdenslager, D.: Prediction theory and Fourier series in several variables. Acta Math. 99, 165–201 (1958)
Janashia, G., Lagvilava, E.: A method of approximate factorization of positive definite matrix functions. Stud. Math. 137, 93–100 (1999)
Koosis, P.: Introduction to H p Spaces. Cambridge University Press, Cambridge (1980)
Rosenblatt, M.: A multidimensional prediction problem. Ark. Mat. 3, 407–424 (1958)
Rosenblum, M.: Vectorial Toeplitz operators and the Fejér-Riesz theorem. J. Math. Anal. Appl. 23, 139–147 (1963)
Wiener, N.: On the factorization of matrices. Comment. Math. Helv. 29, 97–111 (1955)
Wiener, N., Masani, P.: The prediction theory of multivariate stochastic processes, I. Acta Math. 98, 111–150 (1957)
Wiener, N., Akutowicz, E.J.: A factorization of positive Hermitian matrices. J. Math. Mech. 8, 111–120 (1959)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Tom Körner.
Rights and permissions
About this article
Cite this article
Ephremidze, L., Janashia, G. & Lagvilava, E. A Simple Proof of the Matrix-Valued Fejér-Riesz Theorem. J Fourier Anal Appl 15, 124–127 (2009). https://doi.org/10.1007/s00041-008-9051-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00041-008-9051-z