1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Eigenfunction of all shift operators

  1. Oct 8, 2013 #1
    Prove that if a continuous function [itex] e\left( x \right) [/itex] on [itex]\mathbb{R}[/itex] is eigenfunction of all shift operators, i.e. [itex] e\left( x+t \right) = \lambda_t e\left( x \right) [/itex] for all x and t and some constants [itex] \lambda_t [/itex], then it is an exponential function, i.e. [itex] e\left( x \right)= Ce^{ax}[/itex] for some constants C and a.

    Thanks in Advance.
     
  2. jcsd
  3. Oct 8, 2013 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Forum rules: show your work.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted