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Arithmetic progressions -- an operator theoretic view

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  • Motivated by the recent Green--Tao theorem on arithmetic progressions in the primes, we discuss some of the basic operator theoretic techniques used in its proof. In particular, we obtain a complete proof of Szemerédi's theorem for arithmetic progressions of length $3$ (Roth's theorem) and the Furstenberg--Sárközy theorem.
    Mathematics Subject Classification: 47A35, 37A45.


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