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Some Applications

In: Numerical Range of Holomorphic Mappings and Applications

Author

Listed:
  • Mark Elin

    (ORT Braude College, Department of Mathematics)

  • Simeon Reich

    (The Technion - Israel Institute of Technology, Department of Mathematics)

  • David Shoikhet

    (ORT Braude College, Department of Mathematics
    Holon Institute of Technology, Department of Mathematics)

Abstract

The crucial point in our subsequent considerations is the fact that for a holomorphic mapping, even in an infinite-dimensional space, one-sided boundedness of the numerical range already implies that the mapping has unit radius of boundedness. This allows us to study diverse local and global geometric properties and characteristics of holomorphic mappings like Bloch radii, radii of starlikeness and spirallikeness, as well as the problem of analytic extension of semigroups of holomorphic mappings and composition operators discussed below.

Suggested Citation

  • Mark Elin & Simeon Reich & David Shoikhet, 2019. "Some Applications," Springer Books, in: Numerical Range of Holomorphic Mappings and Applications, chapter 0, pages 165-205, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-05020-7_6
    DOI: 10.1007/978-3-030-05020-7_6
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