t-Adic symmetrization map on the harmonic algebra

Harmonic analysis on the p-adic numbers

The ideals of the ring Zp are {0} and pZp, n ≥ 0. From this it follows that Zp is a discrete valuation ring, a principal ideal domain with exactly one maximal ideal, namely pZp; Zp is the valuation ring of Qp with the valuation vp. For n ≥ 1, Zp/pZp is isomorphic as a ring with Z/pZ. |x|p = p−vp(x), dp(x, y) = |x− y|p. With the topology induced by the metric dp, Qp is a locally compact abelian ...

Toeplitz algebra and Hankel algebra on the harmonic Bergman space

In this paper we completely characterize compact Toeplitz operators on the harmonic Bergman space. By using this result we establish the short exact sequences associated with the Toeplitz algebra and the Hankel algebra. We show that the Fredholm index of each Fredholm operator in the Toeplitz algebra or the Hankel algebra is zero.  2002 Elsevier Science (USA). All rights reserved.

The Lie Algebra of Smooth Sections of a T-bundle

In this article, we generalize the concept of the Lie algebra of vector fields to the set of smooth sections of a T-bundle which is by definition a canonical generalization of the concept of a tangent bundle. We define a Lie bracket multiplication on this set so that it becomes a Lie algebra. In the particular case of tangent bundles this Lie algebra coincides with the Lie algebra of vector fie...

Notes on commutative algebra and harmonic analysis

Super algebra and Harmonic Oscillator in Anti de Sitter space

The harmonic oscillator in anti de Sitter space(AdS) is discussed. We consider the harmonic oscillator potential and then time independent Schrodinger equation in AdS space. Then we apply the supersymmetric Quantum Mechanics approach to solve our differential equation. In this paper we have solved Schrodinger equation for harmonic oscillator in AdS spacetime by supersymmetry approach. The shape...