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On a sampling problem for a Bargmann-Fock space

Year 2024, Volume: 53 Issue: 5, 1305 - 1311, 15.10.2024
https://doi.org/10.15672/hujms.1339373

Abstract

The purpose of the present article is to provide geometric sufficient conditions for discrete points to be a sampling sequence for a generalized Hilbert Bargmann-Fock space in several complex variables.

References

  • [1] B. Berndtsson and J. Ortega-Cerdà, On interpolating and sampling in Hilbert spaces of analytic functions, J. reine angew Math. 464, 109-128, 1995.
  • [2] B. Berndtsson and M. Andersson, Henkin-Ramirez formulas with weight factors, Ann. Inst. Fourier. 32 (3), 91-110, 1982.
  • [3] K. Fritzsche and H. Grauert, From Holomorphic Functions to Complex Manifolds, Springer New York, NY, 2002.
  • [4] H. Führ, K. Gröchenig, A. Haimi, A. Klotz and J.L. Romero, Density of sampling and interpolation in reproducing kernel Hilbert spaces, J. Lond. Math. Soc. 96 (3), 663-686, 2017.
  • [5] J. Garnett,Bounded analytic functions, Springer-Verlag New York, 2007.
  • [6] K. Gröchenig, A. Haimi, J. Ortega-Cerdà and J.L. Romero, Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions, J. Funct. Anal. 277 (12), 34 pp, 2019.
  • [7] W. K. Hayman, P. B. Kennedy, Subharmonic Functions, Academic Press, London 1976.
  • [8] L.L. Helms, Potential Theory, Springer Dordrecht Heidelberg London New York, 2009.
  • [9] C.O. Kiselman, Plurisubharmonic functions and potential theory in several complex variables, Development of mathematics 1950-2000, 655-714, Birkhäuser, Basel, 2000.
  • [10] M. Klimek, Pluripotential theory, London Mathematical Society Monographs, Clarendon Press, 266 p, 1991.
  • [11] N. Lindholm, Sampling in weighted $L^p$ spaces of entire functions in $\mathbb C^n$ and estimates of the Bergman kernel, J. Funct. Anal. 182 (2), 390-426, 2001.
  • [12] Yu. Lyubarskii and K. Seip, Sampling and interpolation of entire functions and exponential systems in convex domains, Ark. Mat. 32 (1), 157-193, 1994.
  • [13] J. Ortega-Cerdà and K. Seip, Beurling-type density theorems for weighted $L^p$ spaces of entire functions, J. Anal. Math. 75 (1), 247-266, 1998.
  • [14] K. Seip, Interpolation and sampling in spaces of analytic functions, 33, University Lecture Series. American Mathematical Society, Providence, RI, 2004.
  • [15] K. Seip. Density theorem for sampling and interpolating in the Bargmann-Fock spaces III, Math. Scand. 73, 112-126, 1993.
  • [16] K. Seip and R. Wallstén, Density theorems for sampling and interpolation in the Bargmann-Fock space II, J. reine angew. Math. 429, 107-113, 1992.
  • [17] K. Seip, Density theorem for sampling and interpolating in the Bargmann-Fock spaces I, J. reine angrew Math. 429, 91-106, 1992.
  • [18] K. Seip, Reproducing formulas and double orthogonality in Bargmann and Bergman spaces, SIAM J. Math. Anal. 22 (3), 856-876, 1991.
Year 2024, Volume: 53 Issue: 5, 1305 - 1311, 15.10.2024
https://doi.org/10.15672/hujms.1339373

Abstract

References

  • [1] B. Berndtsson and J. Ortega-Cerdà, On interpolating and sampling in Hilbert spaces of analytic functions, J. reine angew Math. 464, 109-128, 1995.
  • [2] B. Berndtsson and M. Andersson, Henkin-Ramirez formulas with weight factors, Ann. Inst. Fourier. 32 (3), 91-110, 1982.
  • [3] K. Fritzsche and H. Grauert, From Holomorphic Functions to Complex Manifolds, Springer New York, NY, 2002.
  • [4] H. Führ, K. Gröchenig, A. Haimi, A. Klotz and J.L. Romero, Density of sampling and interpolation in reproducing kernel Hilbert spaces, J. Lond. Math. Soc. 96 (3), 663-686, 2017.
  • [5] J. Garnett,Bounded analytic functions, Springer-Verlag New York, 2007.
  • [6] K. Gröchenig, A. Haimi, J. Ortega-Cerdà and J.L. Romero, Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions, J. Funct. Anal. 277 (12), 34 pp, 2019.
  • [7] W. K. Hayman, P. B. Kennedy, Subharmonic Functions, Academic Press, London 1976.
  • [8] L.L. Helms, Potential Theory, Springer Dordrecht Heidelberg London New York, 2009.
  • [9] C.O. Kiselman, Plurisubharmonic functions and potential theory in several complex variables, Development of mathematics 1950-2000, 655-714, Birkhäuser, Basel, 2000.
  • [10] M. Klimek, Pluripotential theory, London Mathematical Society Monographs, Clarendon Press, 266 p, 1991.
  • [11] N. Lindholm, Sampling in weighted $L^p$ spaces of entire functions in $\mathbb C^n$ and estimates of the Bergman kernel, J. Funct. Anal. 182 (2), 390-426, 2001.
  • [12] Yu. Lyubarskii and K. Seip, Sampling and interpolation of entire functions and exponential systems in convex domains, Ark. Mat. 32 (1), 157-193, 1994.
  • [13] J. Ortega-Cerdà and K. Seip, Beurling-type density theorems for weighted $L^p$ spaces of entire functions, J. Anal. Math. 75 (1), 247-266, 1998.
  • [14] K. Seip, Interpolation and sampling in spaces of analytic functions, 33, University Lecture Series. American Mathematical Society, Providence, RI, 2004.
  • [15] K. Seip. Density theorem for sampling and interpolating in the Bargmann-Fock spaces III, Math. Scand. 73, 112-126, 1993.
  • [16] K. Seip and R. Wallstén, Density theorems for sampling and interpolation in the Bargmann-Fock space II, J. reine angew. Math. 429, 107-113, 1992.
  • [17] K. Seip, Density theorem for sampling and interpolating in the Bargmann-Fock spaces I, J. reine angrew Math. 429, 91-106, 1992.
  • [18] K. Seip, Reproducing formulas and double orthogonality in Bargmann and Bergman spaces, SIAM J. Math. Anal. 22 (3), 856-876, 1991.
There are 18 citations in total.

Details

Primary Language English
Subjects Real and Complex Functions (Incl. Several Variables)
Journal Section Mathematics
Authors

Mohammed El Aıdı 0000-0002-3032-0879

Early Pub Date January 10, 2024
Publication Date October 15, 2024
Published in Issue Year 2024 Volume: 53 Issue: 5

Cite

APA El Aıdı, M. (2024). On a sampling problem for a Bargmann-Fock space. Hacettepe Journal of Mathematics and Statistics, 53(5), 1305-1311. https://doi.org/10.15672/hujms.1339373
AMA El Aıdı M. On a sampling problem for a Bargmann-Fock space. Hacettepe Journal of Mathematics and Statistics. October 2024;53(5):1305-1311. doi:10.15672/hujms.1339373
Chicago El Aıdı, Mohammed. “On a Sampling Problem for a Bargmann-Fock Space”. Hacettepe Journal of Mathematics and Statistics 53, no. 5 (October 2024): 1305-11. https://doi.org/10.15672/hujms.1339373.
EndNote El Aıdı M (October 1, 2024) On a sampling problem for a Bargmann-Fock space. Hacettepe Journal of Mathematics and Statistics 53 5 1305–1311.
IEEE M. El Aıdı, “On a sampling problem for a Bargmann-Fock space”, Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 5, pp. 1305–1311, 2024, doi: 10.15672/hujms.1339373.
ISNAD El Aıdı, Mohammed. “On a Sampling Problem for a Bargmann-Fock Space”. Hacettepe Journal of Mathematics and Statistics 53/5 (October 2024), 1305-1311. https://doi.org/10.15672/hujms.1339373.
JAMA El Aıdı M. On a sampling problem for a Bargmann-Fock space. Hacettepe Journal of Mathematics and Statistics. 2024;53:1305–1311.
MLA El Aıdı, Mohammed. “On a Sampling Problem for a Bargmann-Fock Space”. Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 5, 2024, pp. 1305-11, doi:10.15672/hujms.1339373.
Vancouver El Aıdı M. On a sampling problem for a Bargmann-Fock space. Hacettepe Journal of Mathematics and Statistics. 2024;53(5):1305-11.