Advertisement

Mean Periodic Functions on Multidimensional Domains

  • Valery V. VolchkovEmail author
  • Vitaly V. Volchkov
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

The chapter consists of recent developments in the theory of mean periodic functions on domains in ℝ n , n2. The first circle of questions is connected with the John theorem on global uniqueness for integrals of a function f over spheres of radius 1 when supp f is disjoint from |x|1. Similar but much more complex results concerning mean periodic functions are described. In particular, the exact dependence between the order of smoothness of functions satisfying John-type conditions and the set of nonzero coefficients in their Fourier expansions with respect to spherical harmonics is obtained. Further topics include analogues of the Taylor and Laurent expansions for mean periodic functions, some mean periodic extendability results, and the study of the asymptotic behavior of mean periodic functions. The final section is devoted to the problem of approximation on domains in ℝ n of solutions of a convolution equations by exponential solutions. Hörmander’s approximation theorem shows that in the case of convex domains this question is solved positively. Some analogues of Hörmander’s result for domains without the convexity condition are presented.

Keywords

Periodic Function Convergence Theorem Helmholtz Equation Nonzero Function Laurent Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag London Limited 2009

Authors and Affiliations

  1. 1.Mathematical DepartmentDonetsk National UniversityDonetskUkraine

Personalised recommendations