Open AccessSpectra of convolution operators on L p spaces
Author(s) -
Misha Zafran
Publication year - 1975
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.72.9.3285
Subject(s) - multiplier (economics) , mathematics , convolution (computer science) , euclidean space , torus , combinatorics , infinity , transformation (genetics) , pure mathematics , mathematical analysis , chemistry , computer science , geometry , artificial neural network , gene , biochemistry , machine learning , economics , macroeconomics
Let 1 <p < ∞ withp ≠ 2. LetG denote then -torus or Euclideann -space, and let Γ be the dual group ofG . We show the existence of a multiplier transformationT onLp (G)which satisfies the following properties: (a ) the transformT̂ ofT is smooth and vanishes at infinity on Γ; (b ) the spectrum ofT onLp properlycontainsT̂ (Γ)∪{0}.