# On a general bidimensional extrapolation problem

Rodrigo Arocena; Fernando Montana

Colloquium Mathematicae (1993)

- Volume: 64, Issue: 1, page 3-12
- ISSN: 0010-1354

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topArocena, Rodrigo, and Montana, Fernando. "On a general bidimensional extrapolation problem." Colloquium Mathematicae 64.1 (1993): 3-12. <http://eudml.org/doc/210170>.

@article{Arocena1993,

abstract = {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.},

author = {Arocena, Rodrigo, Montana, Fernando},

journal = {Colloquium Mathematicae},

keywords = {generalized moment problems in two dimensions; commutative unitary extensions},

language = {eng},

number = {1},

pages = {3-12},

title = {On a general bidimensional extrapolation problem},

url = {http://eudml.org/doc/210170},

volume = {64},

year = {1993},

}

TY - JOUR

AU - Arocena, Rodrigo

AU - Montana, Fernando

TI - On a general bidimensional extrapolation problem

JO - Colloquium Mathematicae

PY - 1993

VL - 64

IS - 1

SP - 3

EP - 12

AB - 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.

LA - eng

KW - generalized moment problems in two dimensions; commutative unitary extensions

UR - http://eudml.org/doc/210170

ER -

## References

top- [An] T. Ando, On a pair of commutative contractions, Acta Sci. Math. (Szeged) 24 (1963), 88-90. Zbl0116.32403
- [Ar1] R. Arocena, On the extension problem for a class of translation invariant forms, J. Operator Theory, to appear.
- [Ar2] R. Arocena, On the commutant lifting theorem, submitted.
- [B] Ju. M. Berezanskiĭ, Expansions in Eigenfunctions of Selfadjoint Operators, Transl. Math. Monographs 17, Amer. Math. Soc., Providence 1968. Zbl0157.16601
- [C] T. Constantinescu, On a general extrapolation problem, Rev. Roumaine Math. Pures Appl. 32 (1987), 509-521. Zbl0631.47003
- [C-S] Z. Ceauşescu and I. Suciu, Isometric dilations of commuting contractions. II, in: Operator Theory: Adv. Appl. 11, Birkhäuser, 1983, 53-80.
- [D] A. Devinatz, On the extension of positive definite functions, Acta Math. 102 (1959), 109-134. Zbl0100.10601
- [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. Zbl0022.35302
- [N-F] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, 1970. Zbl0201.45003
- [Sa] D. Sarason, Moment problems and operators in Hilbert spaces, in: Proc. Sympos. Appl. Math. 37, Amer. Math. Soc., 1987, 54-70.
- [Se] A. Seghier, Extension de fonctions de type positif et entropie associée. Cas multidimensionnel, Ann. Inst. H. Poincaré, to appear.

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