Function spaces and distributions

  • Sabir Umarov
Part of the Developments in Mathematics book series (DEVM, volume 41)


This chapter is devoted to function and distribution spaces. We first recall definitions of some well-known classical function and distribution spaces, simultaneously introducing the terminology and notations used in this book. Then we introduce (see Section 1.10) a new class of test functions and the corresponding space of distributions (generalized functions), which play an important role in the theory of pseudo-differential operators with singular symbols introduced in Chapter 2 By singular symbols we mean, if not otherwise assumed, symbols singular in dual variables.


Well-known Function Classes Singular Symbols Lizorkin Type Spaces Strict Projective Limit Finite Exponential Type 
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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Sabir Umarov
    • 1
  1. 1.Department of MathematicsUniversity of New HavenWest HavenUSA

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