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Convolution Operators (Vector-Valued Case)

  • R. E. Edwards
  • G. I. Gaudry
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 90)

Abstract

In Chapters 6 and 7 we shall need analogues of the results in Chapter 2 for operators of the type
$${L_K}f\left( x \right) = \int K \left( {x - y} \right)f\left( y \right)dy $$
where now f is a function on G taking values in a Hilbert space ℋ (i.e., a vector-valued function) and K is a function on G taking values in B(ℋ1, ℋ2), the space of bounded linear mappings of ℋ into a second Hilbert space ℋ2 (i.e., an operator-valued kernel).

Keywords

Hilbert Space Convolution Operator Monotone Convergence Theorem Bounded Linear Mapping Plancherel Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • R. E. Edwards
    • 1
  • G. I. Gaudry
    • 2
  1. 1.Institute of Advanced StudiesAustralian National UniversityCanberraAustralia
  2. 2.Flinders UniversityBedford ParkAustralia

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