Journal of Mathematical Sciences

, Volume 237, Issue 3, pp 362–374 | Cite as

Complete Systems of Eigenfunctions of the Vladimirov Operator in L2(Br) and L2(ℚp)

  • A. Kh. BikulovEmail author
  • A. P. Zubarev


We construct new bases of real functions from L2(Br) and from L2(ℚp). These functions are eigenfunctions of the p-adic pseudo-differential Vladimirov operator, which is defined on a compact set Br ⊂ ℚp of the field of p-adic numbers ℚp or, respectively, on the entire field ℚp. A relation between the basis of functions from L2(ℚp) and the basis of p-adic wavelets from L2(ℚp) is found. As an application, we consider the solution of the Cauchy problem with the initial condition on a compact set for a pseudo-differential equation with a general pseudo-differential operator that is diagonal in the basis constructed.


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Authors and Affiliations

  1. 1.Institute of Chemical PhysicsMoscowRussia
  2. 2.Physics DepartmentSamara State Aerospace UniversitySamaraRussia
  3. 3.Physics and Chemistry DepartmentSamara State University of Railway TransportSamaraRussia

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