On rank invariance of moment matrices of nonnegative Hermitian-valued Borel measures on the unit circle

Mathematische Nachrichten

Volumn 263-264, Issue , 2004, Pages 103-132

  Fritzsche, Bernd ^a   Kirstein, Bernd ^a   Lasarow, Andreas ^b  

^a UNIVERSITY OF LEIPZIG   (Germany)

^b MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

Matrix valued rational functionals; Nonnegative Hermitian valued Borel measures on the unit circle

Indexed keywords

EID: 0942278790     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.200310126     Document Type: Article

References (24)

1. A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad, A Szegö theory for rational functions, Report TW 131, Department of Computer Science, K. U. Leuven (1990).
2. A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad, Orthogonal rational functions and interpolatory product rales on the unit circle I - Recurrence and interpolation, Analysis 18, 167-183 (1998).
3. A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad, Orthogonal rational functions and interpolatory product rules on the unit circle II - Quadrature and convergence, Analysis 18, 185-200 (1998).
4. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. Njåstad, Orthogonal Rational Functions, Cambridge Mono, on Applied and Comput. Math. 5 (Cambridge University Press, Cambridge, 1999).
5. A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad, Orthogonal rational functions and interpolatory product rules on the unit circle III - Convergence of general sequences, Analysis 20, 99-120 (2000).
6. P. Delsarte, Y. Genin, and Y. Kamp, Orthogonal polynomial matrices on the unit circle, IEEE Trans. Circuits and Systems CAS-25, 149-160 (1978).
7. P. Delsarte, Y. Genin, and Y. Kamp, Schur parametrization of positive definite block-Toeplitz systems, SIAM J. Appl. Math. 36, 34-46 (1979).
8. M. M. Djrbashian, Orthogonal systems of rational functions on the circle with given set of poles, Dokl. SSSR 147, 1278-1281 (1961) (in Russian).
9. M. M. Djrbashian, Orthogonal systems of rational functions on the circle, Izvestija Akad. Arm. SSR, Ser. Mat. 1, 3-24 (1966) (in Russian).
10. M. M. Djrbashian, Orthogonal systems of rational functions on the circle, Izvestija Akad. Arm. SSR, Ser. Mat. 1, 106-125 (1966) (in Russian).
11. M. M. Djrbashian, A survey on the theory of orthogonal systems and some open problems, in Orthogonal Polynomials: Theory and Practice, edited by P. Nevai, NATO ASI Ser. C: Matem. and Phys. Sci. 294, 135-146 (1990).
12. V. K. Dubovoj, B. Fritzsche, and B. Kirstein, Matricial Version of the Classical Schur Problem, Teubner-Texte zur Mathematik Bd. 129 (Teubner, Stuttgart-Leipzig, 1992).
13. B. Fritzsche and B. Kirstein, An extension problem for non-negative Hermitian block Toeplitz matrices. Part I, Math. Nachr. 130, 121-135 (1987); Part II, Math. Nachr. 131, 287-297 (1987); Part III, Math. Nachr. 135, 319-341 (1988); Part IV, Math. Nachr. 143, 329-354 (1989); Part V, Math. Nachr. 144, 283-308 (1989).
14. B. Fritzsche and B. Kirstein, An extension problem for non-negative Hermitian block Toeplitz matrices. Part I, Math. Nachr. 130, 121-135 (1987); Part II, Math. Nachr. 131, 287-297 (1987); Part III, Math. Nachr. 135, 319-341 (1988); Part IV, Math. Nachr. 143, 329-354 (1989); Part V, Math. Nachr. 144, 283-308 (1989).
15. B. Fritzsche and B. Kirstein, An extension problem for non-negative Hermitian block Toeplitz matrices. Part I, Math. Nachr. 130, 121-135 (1987); Part II, Math. Nachr. 131, 287-297 (1987); Part III, Math. Nachr. 135, 319-341 (1988); Part IV, Math. Nachr. 143, 329-354 (1989); Part V, Math. Nachr. 144, 283-308 (1989).
16. B. Fritzsche and B. Kirstein, An extension problem for non-negative Hermitian block Toeplitz matrices. Part I, Math. Nachr. 130, 121-135 (1987); Part II, Math. Nachr. 131, 287-297 (1987); Part III, Math. Nachr. 135, 319-341 (1988); Part IV, Math. Nachr. 143, 329-354 (1989); Part V, Math. Nachr. 144, 283-308 (1989).
17. B. Fritzsche and B. Kirstein, An extension problem for non-negative Hermitian block Toeplitz matrices. Part I, Math. Nachr. 130, 121-135 (1987); Part II, Math. Nachr. 131, 287-297 (1987); Part III, Math. Nachr. 135, 319-341 (1988); Part IV, Math. Nachr. 143, 329-354 (1989); Part V, Math. Nachr. 144, 283-308 (1989).
18. J. L. Geronimus, On polynomials orthogonal on the unit circle, on the trigonometrical moment problem and on associated functions of classes of Carathéodory-Schur, Mat. USSR-Sb. 15, 99-130 (1944) (in Russian).
19. J. L. Geronimus, On the trigonometric moment problem, Ann. Math. 47, 742-761 (1946).
20. J. L. Geronimus, Orthogonal Polynomials (Fizmatgiz, Moskva, 1958) (in Russian).
21. M. Rosenberg, The square integrability of matrix-valued functions with respect to a non-negative Hermitian measure, Duke Math. J. 31, 291-298 (1964).
22. M. Rosenberg, Operators as spectral integrals of operator-valued functions from the study of multivariate stationary stochastic processes, J. Multivariate Anal. 4, 166-209 (1974).
23. M. Rosenberg, Spectral integrals of operator-valued functions - II. From the study of stationary processes, J. Multi-variate Anal. 6, 538-571 (1976).
24. G. Szegö, Orthogonal Polynomials, Amer. Math. Soc. Coll. Publ. 23 (Providence, R. I., 1939).