Polynomial sequences in discrete nilpotent groups of step 2

Autor:	Ionescu, Alexandru D., Magyar, Akos, Mirek, Mariusz, Szarek, Tomasz Z.
Rok vydání:	2022
Předmět:	Mathematics - Classical Analysis and ODEs
Druh dokumentu:	Working Paper
Popis:	We discuss some of our work on averages along polynomial sequences in nilpotent groups of step 2. Our main results include boundedness of associated maximal functions and singular integrals operators, an almost everywhere pointwise convergence theorem for ergodic averages along polynomial sequences, and a nilpotent Waring theorem. Our proofs are based on analytical tools, such as a nilpotent Weyl inequality, and on complex almost-orthogonality arguments that are designed to replace Fourier transform tools, which are not available in the non-commutative nilpotent setting. In particular, we present what we call a "nilpotent circle method" that allows us to adapt some of the ideas of the classical circle method to the setting of nilpotent groups. Comment: arXiv admin note: substantial text overlap with arXiv:2112.03322
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.14136 Zobrazit plný text záznamu View this record from Arxiv