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Yet Another Approach to Poly-Bergman Spaces

In: Multivariable Operator Theory

Author

Listed:
  • Nikolai Vasilevsk

    (CINVESTAV, Department of Mathematics)

Abstract

We present an alternative characterization of the poly-Bergman and true-poly-Bergman function spaces on the unit disk $${\mathbb {D}}$$ D , based on the pure isometry acting on the standard $$L_2$$ L 2 -space over $${\mathbb {D}}$$ D and the representation of this isometry in terms of differential operators. As an application, we give the representation of the Landau magnetic Hamiltonian in its action in $$L_2$$ L 2 -space over $${\mathbb {D}}$$ D . The true-poly-Bergman spaces appear there as the corresponding eigenspaces.

Suggested Citation

  • Nikolai Vasilevsk, 2023. "Yet Another Approach to Poly-Bergman Spaces," Springer Books, in: Ernst Albrecht & Raúl Curto & Michael Hartz & Mihai Putinar (ed.), Multivariable Operator Theory, pages 861-874, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-50535-5_31
    DOI: 10.1007/978-3-031-50535-5_31
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