On the Inverse to the Harmonic Oscillator

• Let b ( d ) be the Weyl symbol of the inverse to the harmonic oscillator on R- d . We prove that b ( d ) and its derivatives satisfy convenient bounds of Gevrey and Gelfand-Shilov type, and obtain explicit expressions for b ( d ). In the even-dimensional case we characterize b ( d ) in terms of elementary functions. In the analysis we use properties of radial symmetry and a combination of different techniques involving classical a priori estimates, commutator identities, power series and asymptotic expansions.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

46F05

35S05

Secondary 33C10

Primary 35Q40

30Gxx

Ultradistributions

Harmonic oscillator

Gelfand-Shilov estimates

Inverse

Matematik

Mathematics

Publication and Content Type

ref (subject category)

art (subject category)