On a general bidimensional extrapolation problem
Arocena, Rodrigo ; Montana, Fernando
Colloquium Mathematicae, Tome 66 (1993), p. 3-12 / Harvested from The Polish Digital Mathematics Library

Several generalized moment problems in two dimensions are particular cases of the general problem of giving conditions that ensure that two isometries, with domains and ranges contained in the same Hilbert space, have commutative unitary extensions to a space that contains the given one. Some results concerning this problem are presented and applied to the extension of functions of positive type.

Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:210170
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     title = {On a general bidimensional extrapolation problem},
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     volume = {66},
     year = {1993},
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Arocena, Rodrigo; Montana, Fernando. On a general bidimensional extrapolation problem. Colloquium Mathematicae, Tome 66 (1993) pp. 3-12. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv64i1p3bwm/

[000] [An] T. Ando, On a pair of commutative contractions, Acta Sci. Math. (Szeged) 24 (1963), 88-90. | Zbl 0116.32403

[001] [Ar1] R. Arocena, On the extension problem for a class of translation invariant forms, J. Operator Theory, to appear.

[002] [Ar2] R. Arocena, On the commutant lifting theorem, submitted.

[003] [B] Ju. M. Berezanskiĭ, Expansions in Eigenfunctions of Selfadjoint Operators, Transl. Math. Monographs 17, Amer. Math. Soc., Providence 1968. | Zbl 0157.16601

[004] [C] T. Constantinescu, On a general extrapolation problem, Rev. Roumaine Math. Pures Appl. 32 (1987), 509-521. | Zbl 0631.47003

[005] [C-S] Z. Ceauşescu and I. Suciu, Isometric dilations of commuting contractions. II, in: Operator Theory: Adv. Appl. 11, Birkhäuser, 1983, 53-80.

[006] [D] A. Devinatz, On the extension of positive definite functions, Acta Math. 102 (1959), 109-134. | Zbl 0100.10601

[007] [K] M. G. Krein, Sur le problème du prolongement des fonctions hermitiennes positives et continues, C. R. (Doklady) Acad. Sci. URSS (N.S.) 26 (1940), 17-22. | Zbl 0022.35302

[008] [N-F] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, 1970. | Zbl 0201.45003

[009] [Sa] D. Sarason, Moment problems and operators in Hilbert spaces, in: Proc. Sympos. Appl. Math. 37, Amer. Math. Soc., 1987, 54-70.

[010] [Se] A. Seghier, Extension de fonctions de type positif et entropie associée. Cas multidimensionnel, Ann. Inst. H. Poincaré, to appear.