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Sparse Systems of Functions Closed on Large Sets in R N
Author(s) -
Ulanovskii Alexander
Publication year - 2001
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1017/s0024610700001782
Subject(s) - exponential function , mathematics , yield (engineering) , space (punctuation) , interval (graph theory) , basis (linear algebra) , pure mathematics , combinatorics , mathematical analysis , physics , geometry , computer science , thermodynamics , operating system
Let E (Z) = { e inx } n ∈Z denote the trigonometrical exponential system. It is well known that E (Z) forms an orthogonal basis in the space L 2 (0, 2π). In 1964, H. Landau discovered that the trigonometrical system has the following property: certain small perturbations of E (Z) yield exponential systems which are complete in L 2 on any finite union of 2π‐periodic translations of any interval (ε, 2π−ε), 0 < ε < π.