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).



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science