Department of Mathematics

Analysis and PDE

  •  N. K. Nikolski, University of Bordeaux
  •  V.Ya.Kozlov's completeness problem
  •  10/03/2018
  •  4:10 PM - 5:00 PM
  •  C517 Wells Hall

In 1948-1950, V.Ya.Kozlov (1914-2007) stated a series of interesting geometric properties of dilated systems D(f)= {f(kx): k= 1,2,...} in the spaces L^p(0,1). Since that, no proofs were published. In particular, for a Rademacher-Haar-Walsh type generator f= 2-periodic odd extension of the indicator function of (0,a), 0<a<1, the system D(f) was claimed to be complete/incomplete for many particular values of a. We prove all Kozlov's statements and several new, as well as discuss other geometric properties of D(f).

 

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Department of Mathematics
Michigan State University
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