On a general bidimensional extrapolation problem

Rodrigo Arocena; Fernando Montana

Colloquium Mathematicae (1993)

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

Abstract

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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.

How to cite

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Arocena, 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

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  1. [An] T. Ando, On a pair of commutative contractions, Acta Sci. Math. (Szeged) 24 (1963), 88-90. Zbl0116.32403
  2. [Ar1] R. Arocena, On the extension problem for a class of translation invariant forms, J. Operator Theory, to appear. 
  3. [Ar2] R. Arocena, On the commutant lifting theorem, submitted. 
  4. [B] Ju. M. Berezanskiĭ, Expansions in Eigenfunctions of Selfadjoint Operators, Transl. Math. Monographs 17, Amer. Math. Soc., Providence 1968. Zbl0157.16601
  5. [C] T. Constantinescu, On a general extrapolation problem, Rev. Roumaine Math. Pures Appl. 32 (1987), 509-521. Zbl0631.47003
  6. [C-S] Z. Ceauşescu and I. Suciu, Isometric dilations of commuting contractions. II, in: Operator Theory: Adv. Appl. 11, Birkhäuser, 1983, 53-80. 
  7. [D] A. Devinatz, On the extension of positive definite functions, Acta Math. 102 (1959), 109-134. Zbl0100.10601
  8. [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
  9. [N-F] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, 1970. Zbl0201.45003
  10. [Sa] D. Sarason, Moment problems and operators in Hilbert spaces, in: Proc. Sympos. Appl. Math. 37, Amer. Math. Soc., 1987, 54-70. 
  11. [Se] A. Seghier, Extension de fonctions de type positif et entropie associée. Cas multidimensionnel, Ann. Inst. H. Poincaré, to appear. 

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