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NONUNIFORMLY FLAT AFFINE ALGEBRAIC HYPERSURFACES

  • VAMSI PRITHAM PINGALI (a1) and DROR VAROLIN (a2)

Abstract

The relationship between interpolation and separation properties of hypersurfaces in Bargmann–Fock spaces over $\mathbb{C}^{n}$ is not well understood except for $n=1$ . We present four examples of smooth affine algebraic hypersurfaces that are not uniformly flat, and show that exactly two of them are interpolating.

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Vamsi Pritham Pingali is partially supported by the Young Investigator Award and by grant F.510/25/CAS-II/2018(SAP-I) from UGC (Govt. of India).

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References

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[BOC-1995] Berndtsson, B. and Ortega-Cerdá, J., On interpolation and sampling in Hilbert spaces of analytic functions , J. Reine Angew. Math. 464 (1995), 109128.
[GHOR-2018] Gröchenig, K., Haimi, A., Ortega-Cerdá, J. and Romero, J.-L., Strict density inequalities for smapling and interpolation in weighted spaces of holomorphic functions, preprint, 2018, arXiv:1808.02703v1 [math.CA], https://arxiv.org/pdf/1808.02703.pdf.
[L-1997] Lindholm, N., Sampling in weighted L p spaces of entire functions in ℂ n and estimates of the Bergman kernel , J. Funct. Anal. 182(2) (2001), 390426.
[OT-1987] Ohsawa, T. and Takegoshi, K., On the extension of L 2 holomorphic functions , Math. Z. 195(2) (1987), 197204.
[O-2008] Ortega-Cerdá, J., Interpolating and sampling sequences in finite Riemann surfaces , Bull. Lond. Math. Soc. 40(5) (2008), 876886.
[OSV-2006] Ortega-Cerdà, J., Schuster, A. and Varolin, D., Interpolation and sampling hypersurfaces for the Bargmann–Fock space in higher dimensions , Math. Ann. 335(1) (2006), 79107.
[OS-1998] Ortega-Cerdà, J. and Seip, K., Beurling-type density theorems for weighted L p spaces of entire functions , J. Anal. Math. 75 (1998), 247266.
[PV-2016] Pingali, V. and Varolin, D., Bargmann–Fock extension from singular hypersurfaces , J. Reine Angew. Math. 717 (2016), 227249.
[SV-2008] Schuster, A. and Varolin, D., Interpolation and sampling for generalized Bergman spaces on finite Riemann surfaces , Rev. Mat. Iberoam. 24(2) (2008), 499530.
[S-1992] Seip, K., Density theorems for sampling and interpolation in the Bargmann–Fock space. I , J. Reine Angew. Math. 429 (1992), 91106.
[S-1993] Seip, K., Beurling type density theorems in the unit disk , Invent. Math. 113(1) (1993), 2139.
[SW-1992] Seip., K. and Wallsén, R., Density theorems for sampling and interpolation in the Bargmann-Fock space. II , J. Reine Angew. Math. 429 (1992), 107113.
[V-2008] Varolin, D., A Takayama-type extension theorem , Compos. Math. 144(2) (2008), 522540.
[V-2016] Varolin, D., Bergman interpolation on finite Riemann surfaces. Part II: Poincaré-hyperbolic case , Math. Ann. 366(3–4) (2016), 11371193.
[V-2018] Varolin, D., Bergman interpolation on finite Riemann surfaces. Part I: Asymptotically flat case , J. Anal. Math. 136(1) (2018), 103149.
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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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