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Session 17. Functional Analysis: relations to Complex Analysis and PDE
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Projective description for inductive limits of spaces of differentiable functions |
Jochen Wengenroth, University Trier, Germany
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Weighted inductive limits of spaces of continuous function
\[
\mathcal V C(X)=\{ f\in C(X): \exists\; n\in \mathbb{N}\; \sup\{v_{n}(x) |f(x)|\} <\infty\}
\]
for suitable sequences of weight functions
appear in connection with several analytical problems and are well investigated since the seminal work [1] of Bierstedt, Meise, and Summers from 1982.
In particular, under realistic assumptions there is a concrete description of all continuous semi-norms of the space endowed with its natural inductive limit topology.
Using only abstract homological methods, we will provide an analogous description for similar weighted inductive limits of \(C^m\) functions. As a very particular case,
this contains recent results of Ortner and Wagner [2] about spaces \(\mathscr O_c^m\) introduced by H
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References- K.-D. Bierstedt, R. Meise, W. Summers, A projective description of weighted inductive limits ,
Trans. Amer. Math. Soc. 272 (1982), 107-160.
- N. Ortner, P. Wagner, On the spaces \(\mathscr O_c^m\) of John Horváth , J. Math. Anal. Appl. 415 (2014), 62-74.
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