Chapter 10 Translation Invariance in Real Analysis

  1. Leonard F. Richardson

Published Online: 29 JUN 2009

DOI: 10.1002/9780470501153.ch10

Measure and Integration: A Concise Introduction to Real Ananysis

Measure and Integration: A Concise Introduction to Real Ananysis

How to Cite

Richardson, L. F. (2009) Chapter 10 Translation Invariance in Real Analysis, in Measure and Integration: A Concise Introduction to Real Ananysis, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470501153.ch10

Publication History

  1. Published Online: 29 JUN 2009
  2. Published Print: 17 JUN 2009

ISBN Information

Print ISBN: 9780470259542

Online ISBN: 9780470501153

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Keywords:

  • Schwartz functions;
  • Fourier analysis;
  • orthonormal basis for L2 (��);
  • closed invariant subspaces of L2 (��);
  • Hilbert space;
  • Fourier transform;
  • Fourier inversion;
  • direct integrals;
  • irreducibility of L2(ℝ);
  • Heisenberg group

Summary

This chapter contains sections titled:

  • An Orthonormal Basis for L2(��)

  • Closed, Invariant Subspaces of L2(��)

  • Schwartz Functions: Fourier Transform and Inversion

  • Closed, Invariant Subspaces of L2(��)

  • Irreducibility of L2(ℝ) Under Translations and Rotations