Two Distinguished Subspaces of Product BMO and Nehari-Aak Theory for Hankel Operators on The Torus

Integral Equations and Operator Theory

Volumn 26, Issue 3, 1996, Pages 273-304

  Cotlar, Mischa ^a   Sadosky, Cora ^b  

^a FACULTAD DE CIENCIAS   (Venezuela)

^b HOWARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001295077     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf01306544     Document Type: Article

References (20)

1. [AAK] V. M. Adamjan, V. Z. Arov and M. G. Krein, Analytic properties of Schmidt pairs of a Hankel operator and generalized Schur-Takagi problem, Mat. Sbornik 86 (1971), 33-73.
2. 2 and lifting properties, Adv. Math. Suppl. Stud. 7A (1981), 95-128.
3. [Ag] Jim Agler, Interpolation, J. Funct. Anal., to appear.
4. [Am] E. Amar, Les théorèmes de Schwarz-Pick et Nevanlinna en plusieurs variables complexes, dans Thèse, Université de Paris-Sud, Orsay, 1977.
5. [AhC] P. Ahern and D. N. Clark, Invariant subspaces and analytic continuation in several variables, J. Math. Mech. 19 (1969/70), 963-969.
6. [BH] J. Ball and W. Helton, A Beurling-Lax theorem for the Lie group U(m, n) which contains most classical interpolation theory, J. Operator Theory 9 (1983), 107-142.
7. 1 and BMO on the bi-disc, Ann. of Math. 112 (1980), 179-201.
8. p theory on product spaces, Bull. Amer. Math. Soc. 12 (1985), 1-43.
9. [CLW] Brian Cole, Keith Lewis and John Wermer, Pick conditions on a uniform algebra and von Neumann inequality, J. Funct. Anal. 107 (1992), 235-254.
10. p of the bidimensional torus, Contemp. Math. 107 (1990), 19-37.
11. [CS2] M. Cotlar and C. Sadosky, Abstract, weighted and multi-dimensional AAK theorems, and the singular numbers of Sarason commutants, Int. Eqs. and Op. Th. 17 (1993), 169-201.
12. [CS3] M. Cotlar and C. Sadosky, Nehari and Nevanlinna-Pick problems and homomorphic extensions in the polydisk in terms of restricted BMO, J. Funct. Anal. 121 (1994), 205-210.
13. [CS4] M. Cotlar and C. Sadosky, A polydisk version of Beurling's characterization for invariant subspaces of finite cotype, Proc. Intl. Congress on Complex and Hypercomplex Analysis, Mexico 1994, to appear.
14. [CW] B. Cole and J. Wermer, "Pick interpolation, von Neumann inequalities and hyperconvex sets," pp. 98-129 in Complex Potential Theory, P. M. Gauthier (ed.), NATO Adv. Sci. Inst. Ser. C 439, Kluwer, Dordrecht, 1994.
15. [HS] H. Helson and G. Szeg̈, A problem in prediction theory, Ann. Math. Pure Appl. 51 (1960), 107-138.
16. [N] Z. Nehari, On bilinear forms, Ann. of Math. 68 (1957), 153-162.
17. [Ni] N. K. Nikolskii, Treatise on the Shift Operator, Springer, Berlin, 1986.
18. [P] G. Pick, Über die Beschränkungen analytischer Funktionen, welche durch vorgegebene Funktionswerte bewirht werden, Math. Ann. 77 (1916), 7-23.
19. [T1] S. Treil, The theorem of Adamjan-Arov-Krein: Vector variant, Pnbl. Seminar LOMI Leningrad 141 (1985), 56-72 (in Russian).
20. [T2] S. Treil, Hankel operators, imbedding theorems and bases of covariant subspaces of the shift of higher multiplicity, Algebra and Analysis 1 (1989), 200-234 (in Russian).