Norms of embeddings between quadratically weighted spaces of holomorphic functions

Joe Viola (1, 2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 AEDP - Equations aux dérivées partielles

We consider spaces of holomorphic functions which are squareintegrable against a Gaussian weight, which appear in the theory of metaplectic FBI-Bargmann transforms. We identify the operator norm of embeddings between two such spaces, by relating these embeddings to Fourier integral operators with complex phase.

Domaines: Equations aux dérivées partielles [math.AP]; Variables complexes [math.CV]

Joe Viola. Norms of embeddings between quadratically weighted spaces of holomorphic functions. 2022. ⟨hal-03794681⟩