A conjecture for some partial differential operators onL 2(R n)

  • Pl. Muthuramalingam


OnX =L 2(R n), letQ = (Q 1,Q 2,…,Q n) andP = (P 1,P 2, …,P n) be the operators given by (Q jf) (x) =x jf(x),P j = - i∂/∂x j. For anyC functionh:R nR putH 0 =h(P) andH =H 0 + (1 +Q 2), where δ > 1/2. By the method of scattering theory we prove thatH ac, the absolutely continuous part ofH is unitarily equivalent toH 0 when (a)n = 1 and (b) forn ≥ 2, whenh is in a large class of polynomials. It is conjectured that the results are true for any polynomialh. We use the techniques of Enss’ method and the idea of bound states for momentum.


Partial differential operators scattering theory Enss’ method 


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Copyright information

© Indian Academy of Sciences 1994

Authors and Affiliations

  • Pl. Muthuramalingam
    • 1
  1. 1.Indian Statistical InstituteBangaloreIndia

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