The multiplicative Weyl functional calculus
✍ Scribed by Robert F.V Anderson
- Publisher
- Elsevier Science
- Year
- 1972
- Tongue
- English
- Weight
- 689 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
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## Abstract In this article we apply the __S__(__M__, __g__)–calculus of L. Hörmander and, in particular, results concerning the spectral invariance of the algebra of operators of order zero in ℒ︁(__L__^2^(ℝ^__n__^)) to study generators of Feller semigroups. The core of the article is the proof of
In this paper, we will introduce a new multiplicative functional Eq. 1 and prove Ž . that the given equation is equivalent to the well known ''original'' one, f xy s Ž . Ž . Ž . f x f y . Moreover, we will investigate the stability problem of Eq. 1 in the sense of R. Ger.
Let # be the Gauss measure on R d and L the Ornstein Uhlenbeck operator, which is self adjoint in L 2 (#). For every p in (1, ), p{2, set , p \*=arc sin |2Âp&1| and consider the sector The main result of this paper is that if M is a bounded holomorphic function on S ,\* p whose boundary values on S