Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Density theorems for sampling and interpolation in the Bargmann-Fock space

Author(s): Kristian Seip
Journal: Bull. Amer. Math. Soc. 26 (1992), 322-328.
MSC (2000): Primary 30D10, 30E05, 46E20; Secondary 81D30
MathSciNet review: 1136138
Retrieve article in: PDF

References | Similar articles | Additional information

References:

*
{bagrza}H. Bacry, A. Grossmann, and J. Zak, {\em Proof of the completeness of lattice states in the $kq$-representation},Phys. Rev. B {\bf 12} (1975), 1118--1120. MR
*
{babugikl}V. Bargmann, P. Butero, L. Girardello, and J. R.Klauder, {\em On the completeness of coherent states},Rep. Mod. Phys. {\bf 2} (1971), 221--228. MR 290680
*
{be}A. Beurling, {\em The collected works of Arne Beurling,vol.} 2 {\em Harmonic analysis}(L. Carleson, P. Malliavin, J. Neuberger, and J. Wermer, eds.),Birkh\"{a}user, Boston, MA, 1989, pp. 341--365. MR 1057614
*
{da2}I. Daubechies, {\em The wavelet transform, time-frequencylocalization and signal analysis}, IEEE Trans. Inform. Theory{\bf 36} (1990), 961--1005. MR 1066587
*
{dagr} I. Daubechies and A. Grossmann, {\em Frames in the Bargmann space of entire functions}, Comm. Pure Appl. Math., {\bf 41} (1988), 151--164. MR 924682
*
{dagrme} I. Daubechies, A. Grossmann, and Y. Meyer,{\em Painless nonorthogonal expansions}, J. Math. Phys.{\bf 27} (1986), 1271--1283. MR 836025
*
{dusc}R. J. Duffin and A. C. Schaeffer, {\em A class of nonharmonicFourier series}, Trans. Amer. Math. Soc. {\bf 72} (1952), 341--366. MR 47179
*
{fo} G. B. Folland, {\em Harmonic analysis in phase space,}Princeton Univ. Press, Princeton, NJ, 1989. MR 983366
*
{grwa}K. Gr\"{o}chenig and D. Walnut, {\em A Riesz basis forthe Bargmann-Fock space related to sampling and interpolation},Ark. Mat. (to appear). MR
*
{japero} S. Janson, J. Peetre, and R. Rochberg,{\em Hankel forms and the Fock space}, Revista Mat. Iberoamer.{\bf 3} (1987), 61--138. MR 1008445
*
{la}H. J. Landau, {\em Necessary density conditions for samplingand interpolation of certain entire functions}, Acta Math.{\bf 117} (1967), 37--52. MR 222554
*
{ly}Y. Lyubarskii, {\em Frames in the Bargmann space ofentire functions}, manuscript, 1990. MR
*
{ne}J. von Neumann, {\em Foundations of quantum mechanics},Princeton Univ. Press, Princeton, NJ, 1955. MR 66944
*
{pe} A. M. Perelomov, {\em On the completeness of a system ofcoherent states}, Theor. Math. Phys. {\bf 6} (1971), 156--164. MR 475444
*
{se} K. Seip,{\em Reproducing formulas and double orthogonality in Bargmann and Bergmanspaces}, SIAM J. Math. Anal. {\bf 22} (1991), 856--876. MR 1091688
*
{se2} \bysame {\em Regular sets of sampling and interpolation for weighted Bergman spaces},Proc. Amer. Math. Soc. (to appear). MR 1111222
*
{se3} \bysame {\em Density theorems for sampling and interpolationin the Bargmann-Fock space} I, J. Reine Angew. Math. (to appear). MR
*
{se4}K. Seip, {\it Beurling type density theorems in the unit disk},manuscript, 1992. MR 1223222
*
{sewa}K. Seip and R. Wallst\'{e}n, {\em Density theorems for samplingand interpolation in the Bargmann-Fock space} II, J. Reine Angew.Math. (to appear). MR 1173118
*
{yo}R. M. Young, {\em An introduction to nonharmonic Fourierseries}, Academic Press, New York, 1980. MR 591684

Similar Articles:

Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 30D10, 30E05, 46E20, 81D30

Retrieve articles in all Journals with MSC (2000): 30D10, 30E05, 46E20, 81D30


Additional Information:

DOI: 10.1090/S0273-0979-1992-00290-2
PII: S 0273-0979(1992)00290-2