Let H be a real or complex Hilbert space, and let ) 0. A functional f on H is < Ε½ . Ε½ . Ε½ .< called an -approximately linear functional if f x q y y f x y f y F Ε½< < 5 5 < < 5 5. x q y for all scalars , and all vectors x, y g H. If such a functional f is bounded then there exists a continuous linea
Harmonic functions on Hilbert space
β Scribed by Victor Goodman
- Publisher
- Elsevier Science
- Year
- 1972
- Tongue
- English
- Weight
- 965 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract In this paper we consider the problem of constructing in domains Ξ©of β^__m__+1^ with a specific geometric property, a conjugate harmonic __V__ to a given harmonic function __U__, as a direct generalization of the complex plane case. This construction is carried out in the framework of C
As is well-known, there is a close and well-deΓΏned connection between the notions of Hilbert transform and of conjugate harmonic functions in the context of the complex plane. This holds e.g. in the case of the Hilbert transform on the real line, which is linked to conjugate harmonicity in the upper