Vector-valued holomorphic and harmonic functions

DOI10.1515/conop-2016-0007zbMath1350.46031OpenAlexW2400851303MaRDI QIDQ283907

Wolfgang Arendt

Publication date: 17 May 2016

Published in: Concrete Operators (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/conop-2016-0007

zbMATH Keywords

Dirichlet problemBanach spaceharmonic functionsholomorphic functionsVitali's theorem

Mathematics Subject Classification ID

Spaces of vector- and operator-valued functions (46E40) Holomorphic maps in nonlinear functional analysis (46T25) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20) Generalizations of potential theory (31C99)

Related Items (6)

The Perron solution for vector-valued equations ⋮ On sequence space representation and extension of vector-valued functions ⋮ Gâteaux or Fréchet differentiable norms in duals of complex interpolation spaces ⋮ Elliptic problems and holomorphic functions in Banach spaces ⋮ Unnamed Item ⋮ Extension of vector-valued functions and weak-strong principles for differentiable functions of finite order

Cites Work

• Vector-valued holomorphic functions revisited
• Perturbation theory for linear operators.
• Sets of uniqueness for harmonic and analytic functions and inverse problems for wave equations
• Vector-valued Laplace Transforms and Cauchy Problems
• From Forms to Semigroups
• Analytic Functions into Banach Spaces and a New Characterization for Isomorphic Embeddings
• A weak criterion for vector-valued holomorphy
• Extension of vector-valued holomorphic and harmonic functions
• Elliptic operators with infinite-dimensional state spaces
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