manuscripta mathematica

, Volume 34, Issue 1, pp 45–70

The C*-algebra of the N-dimensional harmonic oscillator

  • Houshang H. Sohrab

DOI: 10.1007/BF01168709

Cite this article as:
Sohrab, H.H. Manuscripta Math (1981) 34: 45. doi:10.1007/BF01168709


In this paper we study the Fredholm thoery of a C*-algebraOl of o-order pseudo-differential operators on L2(ℝn). IfK denotes the ideal of all compact operators of L2, the algebraOl will be generated by (i) the idealK, (ii) a function algebra CS(ℝn) and (iii) by the bounded operators xjΛ, DjΛ, j=1,...,n, Λ= H−1/2, H=1+¦x¦2−Δ. We show thatOl/K is a commutative C*-algebra with identity and obtain its Gelfany space M. This provides Fredholm criterion and index formula for a graded algebra of partial differential operators including all oeprators with polynomial coefficients. We also give Fredholm criterion and index formula for systems of such operators.

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Houshang H. Sohrab
    • 1
  1. 1.c/o Dr. S. Mozayeny45 OsnabrückFed. Rep. of Germany