Abstract
We study entire functions on infinite-dimensional spaces. The basis is the study of spaces of Gateaux holomorphic functions that are bounded on certain subsets (bounded entire functions). The main goal is to characterize the Fourier image of the corresponding spaces of generalized entire functions (ultra-distributions) by an infinite-dimensional Paley-Wiener theorem. We introduce entire functions of exponential type and prove a generalization of the classical Paley-Wiener theorem. The crucial point of our theory is the dimension-invariant estimate given by Lemma 4.12.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
