Introductory Ideas

  • Steven G. Krantz
Part of the Graduate Texts in Mathematics book series (GTM, volume 268)


In the early days of functional analysis—the early twentieth century—people did not yet know what a Banach space was nor a Hilbert space. They frequently studied a particular complete, infinite-dimensional space from a more abstract point of view. The most common space to be studied in this regard was of course L 2. It was when Stefan Bergman took a course from Erhard Schmidt on L 2 of the unit interval I that he conceived of the idea of the Bergman space of square-integrable holomorphic functions on the unit disc D. And the rest is history.


Manifold Posit DIF3 


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Steven G. Krantz
    • 1
  1. 1.Department of MathematicsWashington University at St. LouisSt. LouisUSA

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