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

Convolution 

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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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