spectral theory

tehniobium_1

Quite a tricky little Hanjie - can be done without guessing or temporaries though! Good luck.

Explanation of the image:
If A is a normal operator acting on a Hilbert Space H with spectrum I, and f is a Borel function on I, we can define the operator f(A) by the forumla in the image. This "Borel function calculus" is an important consequence of the spectral theory of these operators, and an invaluable tool in the treatment of such operators.

Reference: Kadison & Ringrose's "Fundamentals of the theory of operator algebras".
See also: https://en.wikipedia.org/wiki/Borel_functional_calculus

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  • Strange_Victini
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    "Spectral theory is connected with the investigation of localized vibrations of a variety of different objects, from atoms and molecules in chemistry to obstacles in acoustic waveguides. These vibrations have frequencies, and the issue is to decide when such localized vibrations occur, and how to go about computing the frequencies. This is a very complicated problem since every object has not only a fundamental tone but also a complicated series of overtones, which vary radically from one body to another." - Wikipedia

    And I still don't understand it at all! :D.
    July 6, 2017, 8:49 pm
  • Sparks
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    Thanks for a difficult puzzle.
    July 7, 2017, 12:00 am
  • tehniobium_1
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    @Rawr: You're welcome! There was actually an earlier version that was EVEN harder, but unfortunately ended with 4-5 dots that couldn't be determined logically right at the end. Glad you enjoyed it.
    July 7, 2017, 12:07 pm
  • grahamoxxx
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    Great.
    July 8, 2017, 11:31 pm
  • Max3710
    Max3710
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    Ah, spectral theory, I learned a little at university :) Really enjoyable, thank you Tehniobium.
    July 9, 2017, 2:35 pm