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Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.

3 votes
Accepted

holomorphy in infinite dimensions (holomorphic families of operators)

In addition to the information given by user bathalf15320, I think that a bit more information on the Banach space case could be useful: Here is a very general theorem about vector valued functions: T …
Jochen Glueck's user avatar
6 votes
Accepted

Does uniform boundedness carry over from the non-negative real axis to closed sectors of $\m...

There is a one-dimensional counterexample: Consider the analytic semigroup $z \mapsto e^{iz}$. This semigroup is bounded on the non-negative real line, but it is not bounded on any sector $\Delta_\del …
Jochen Glueck's user avatar
2 votes

Vector valued disc "algebra"

Edit 2018-08-08: Partial positive result added (Theorem 2). First, here is a counterexample for the case of weak${}^*$-continuity: Counterexample 1. Let $E = \ell^\infty := \ell^\infty(\mathbb{N}_0) …
Jochen Glueck's user avatar
33 votes
Accepted

Why should I look at the resolvent formalism and think it is a useful tool for spectral theory?

Preliminary remark. As mentioned in the comments, I find the notion "resolvent formalism", as well as the description in the Wikipedia article, rather misleading - resolvents are not somekind of forma …
Jochen Glueck's user avatar