Associated weights and spaces of holomorphic functions
When treating spaces of holomorphic functions with growth conditions, one is led to introduce associated weights. In our main theorem we characterize, in terms of the sequence of associated weights, several properties of weighted (LB)-spaces of holomorphic functions on an open subset $G ⊂ ℂ^N$ which play an important role in the projective description problem. A number of relevant examples are provided, and a "new projective description problem" is posed. The proof of our main result can also serve to characterize when the embedding of two weighted Banach spaces of holomorphic functions is compact. Our investigations on conditions when an associated weight coincides with the original one and our estimates of the associated weights in several cases (mainly for G = ℂ or D) should be of independent interest.
- 46A04: Locally convex Fr\'echet spaces and (DF)-spaces
- 32A22: Nevanlinna theory (local); growth estimates; other inequalities
- 32A30: Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30)
- 46M40: Inductive and projective limits
- 46A13: Spaces defined by inductive or projective limits (LB, LF, etc.)
- 30D15: Special classes of entire functions and growth estimates
- 46A11: Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
- 46E10: Topological linear spaces of continuous, differentiable or analytic functions
- FB 17, Mathematik, Universität-Gesamthochschule-Paderborn, D-33095 Paderborn, Germany
- Department of Mathematics, P.O. Box 4 (Yliopistonkatu 5), FIN-00014 University of Helsinki, Finland
- Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, E-46071 Valencia, Spain
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