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Riesz bases of reproducing kernels in Fock-type spaces

  • Alexander Borichev (a1) and Yurii Lyubarskii (a2)

In a scale of Fock spaces with radial weights ϕ we study the existence of Riesz bases of (normalized) reproducing kernels. We prove that these spaces possess such bases if and only if ϕ(x) grows at most like (log x)2.

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1. A. Borichev , R. Dhuez and K. Kellay , Sampling and interpolation in large Bergman and Fock spaces, J. Funct. Analysis 242(2) (2007), 563606.

2. F. Holland and R. Rochberg , Bergman kernel asymptotics for generalized Fock spaces, J. Analysis Math. 83 (2001), 207242.

3. K. Isaev and R. Yulmukhametov , The absence of unconditional bases of exponentials in Bergman spaces on non-polygonal domains, Izv. Math. 71 (2007), 6990.

5. Yu. Lyubarskii and E. Malinnikova , On approximation of subharmonic functions, J. Analysis Math. 83 (2001), 121149.

6. Yu. Lyubarskii and K. Seip , Sampling and interpolation of entire functions and exponential systems in convex domains, Ark. Mat. 32 (1994), 157193.

7. N. Nikolski , Treatise on the shift operator (Springer, 1986).

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Journal of the Institute of Mathematics of Jussieu
  • ISSN: 1474-7480
  • EISSN: 1475-3030
  • URL: /core/journals/journal-of-the-institute-of-mathematics-of-jussieu
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