Abstract
We now introduce “asymptotic spaces” of holomorphic functions on \(\mathbb {C}^*\) or on Σ which have prescribed descent to 0 for λ →∞ and/or for λ → 0; for this purpose we will cover \(\mathbb {C}^*\) by a sequence \((S_k)_{k\in \mathbb {Z}}\) of annuli, the descent of the functions described by these spaces will be uniform on each of these annuli S k (up to a factor w(λ)s).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In most of our applications, we will have \(G \in \{\mathbb {C}^*,V_\delta \}\) resp. \(\widehat {G}\in \{\varSigma ,\widehat {V}_\delta \}\), p ∈{2, ∞} and s ∈{0, 1}.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Klein, S. (2018). Asymptotic Spaces of Holomorphic Functions. In: A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation. Lecture Notes in Mathematics, vol 2229. Springer, Cham. https://doi.org/10.1007/978-3-030-01276-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-01276-2_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-01275-5
Online ISBN: 978-3-030-01276-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)