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DTSTART;TZID=America/Toronto:20260114T093000
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URL:https://uwaterloo.ca/pure-mathematics/events/phd-defence-1
SUMMARY:PhD. Defence
CLASS:PUBLIC
DESCRIPTION:ZHIHAO ZHANG\, UNIVERSITY OF WATERLOO\n\n_Translation-Invariant
  Function Algebras of Compact Groups_\n\nLet G be a compact group and let 
 Trig(G) denote the algebra of\ntrigonometric polynomials of G. For a trans
 lation-invariant subalgebra\nA of Trig(G)\, one can consider the completio
 ns of A under the uniform\nnorm and the Fourier norm. We show in Chapter 2
  using techniques\ndeveloped by Gichev that both completions have the same
  Gelfand\nspectrum\, answering a question posed in a paper of Spronk and S
 tokke.\nIn the same paper\, a theorem describing of the Gelfand spectrum o
 f the\nFourier completion of finitely-generated such algebras A was given.
  In\nChapter 3\, we extend this theorem to the case of countably-generated
 \,\ntranslation-invariant subalgebras\, A. In Chapter 4\, we give a brief\
 noverview of the Beurling--Fourier algebra\, a weighted variant of the\ncl
 assical Fourier algebra studied by Ludwig\, Spronk and Turowska. The\naddi
 tion of a weight for these particular algebras invites new\nspectral data 
 in contrast to its classical counterpart. In Chapter 5\,\nwe show for Beur
 ling--Fourier algebras of compact abelian groups\, G\,\nthat its weight ca
 n be used to construct a seminorm on a real vector\nspace generated by the
  dual of G that remembers the spectral data of\nthe algebra.\n\nMC 2009
DTSTAMP:20260503T115816Z
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